Insulatable, insulative framework apparatus and methods of making and using same

ABSTRACT

A building framework is disclosed herein having a first structural member, a second structural member, and a third structural member disposed between the first and second structural members, a first web member connecting the first and third structural members in a spaced apart relationship, and a second web member connecting the second and third structural members in a spaced apart relationship. The first web member is positioned relative to the second web member such that the shortest distance between the first web member and second web member is greater than or equal to 5 times the thickness of the third structural member. Additional products, systems, and methods also are disclosed.

RELATED APPLICATIONS

The present application claims priority to U.S. Provisional PatentApplication No. 62/720,808 that was filed Aug. 21, 2018, the contents ofwhich is hereby incorporated by reference in its entirety.

OTHER PUBLICATIONS

-   [1] “Measure Guideline: Wood Window Repair, Rehabilitation, and    Replacement” by Peter Baker, Building America Report—120, Building    Science Press, 2012. Retrieved from    https://www.buildingscience.com/documents/bareports/ba-1203-wood-window-repair-rehabilitation-replacement/view.-   [2] “Heat and Mass Transfer: a practical approach—3rd edition”    by Y. A. Cengel, McGraw-Hill, New York, N.Y. (2003).-   [3] “Acoustic Absorption in Porous Materials,” by Kuczmarski et. al,    NASA/TM-2011-216995.-   [4] ASTM Designation C168-97 “Standard Terminology Relating to    Insulating Materials” reprinted by the American Society for Testing    and Materials

TECHNICAL FIELD

This disclosure relates generally to construction, and more particularlyto the construction of insulating structures with structural elements.

Structural elements used in the construction of walls, ceilings, floors,doors and windows are generally made from wood or other compositematerial. Wood conducts energy, mostly in the form of heat, in alldirections. However, the conductivity along the grain of the wood isabout 2.5 times greater than the conductivity in a direction across thegrain. A typical wall stud allows energy to flow from the stud surfacehaving a first panel attached to the opposing stud surface having asecond panel attached. This allows energy to flow in a direct path fromone panel to the other through the stud with no insulative materialresisting the flow of energy. Particularly in a stud which has studedges separated by a joining member, the joining member allows a directpath of energy between the opposing stud surfaces. In an effort toimprove resistance to energy flow by placing the joining memberdiagonally between the stud inside and outside portions to extending thejoining member length, the energy flow may actually increase since theenergy flow in the direction of the wood grain is 2.5 times the flowagainst the grain.

There is a need for a structural member that increases the resistance toenergy flow from one edge that contacts a first panel to an opposingsurface that contacts a second panel. The structural member describedherein provides the resistance to energy flow which improves the overallinsulative properties of the structure built with these structuralmembers.

Buildings account for approximately 30% of global energy consumption.The structural frame of a residential building framed with solid sawnlumber accounts for approximately 20% of the total inefficiency if nocorrective measures are taken. This problem is called thermal bridging.Windows are a source of even greater inefficiency. For example, acalculation performed by Building Science Corporation shows that anominal R-value of 15 (° F.·ft2 per BTUh) wall has an actual R-valueeffectively equal to 7 (° F.·ft2 per BTUh) producing an inefficiency ofmore than 50% when vinyl-frame double-pane windows with a nominalR-value of 5 (° F.·ft2 per BTUh) constitute just 18% of the total wallarea [1].

Experimental application of the present embodiments and methods usingoff-the-shelf parts such as common 2×4 lumber and glass produces a 2×4wall with an actual R-value of 15 (° F.·ft2 per BTUh), 0% inefficiency,and full efficiency (see FIG. 36F) relative to the nominal R-value of 15(° F.·ft2 per BTUh) for the wall (see Table 5) and more impressively awindow with an actual R-value of 15 (° F.·ft² per BTUh), 0% inefficiencydue to thermal bridging, and full efficiency (see FIG. 36H) relative tothe nominal R-value of 15 (° F.·ft² per BTUh) for the wall. Retrofittingevery building with windows with full energy-efficiency relative to therest of the building envelope over the course of 20 years alone wouldhave a significant impact on the global energy consumption of buildings.

The embodiments and methods described herein represent a powerful way toaddress the problem and cost effectively construct buildings that canmaintain a comfortable indoor environment via passive radiative heatingby the sun in winter and passive radiative cooling to the sky in summer.The industry standard for calculating the energy efficiency of buildingsis based on one-dimensional models of heat transfer. Due to this fact arather lengthy disclosure is provided in order to explain how tointuitively understand heat flow in three dimensions and how toaccurately correct the standard one-dimensional heat flow models tofully capture the effects of three-dimensional heat flow and thermalbridging.

For instance, the industry standard one-dimensional models of heat flowdo not allow for the funneling type of effect where heat runs in apartially lateral direction across a wall into a thermal bridge andbypasses insulation (see wall assembly 3602 in FIG. 36B). For thatreason, the effect of thermal bridging is usually underestimated. Themore efficient a building the greater the impact of thermal bridging onthe percentage of heat loss and heat gain. Industry standardtwo-dimensional models and three-dimensional models of heat transferimplemented by computer programs are inaccessible to most trades,require lengthy setup time, and yield little physical insight into theproblems and solutions when actually used.

In contrast, this disclosure defines measurement paths (metric paths)that a builder can actually draw with a pencil and measure with ameasuring tape (see FIGS. 1D-1H, FIG. 2AH, and FIG. 2A1). Aftermeasuring the length of the metric path in inches (mm) for heat flow thebuilder can simply multiply by the R-value per inch (R_(SI) per mm) toobtain, the structurally insulative R-value, R_(sval) (R_(SIs)), inimperial (metric) units. Conservatively this method can be as rigorousas a fully developed three-dimensional heat flow calculation but has theadvantage of simplicity and greater physical insight into the paths ofleast resistance along which heat can and does actually flow in reality.

With experience, and based on this disclosure, the conscientious buildermay come to appreciate that more indirect metric paths lead to largerstructurally insulative R-values and more direct paths lead to smallerstructurally insulative R-values. An experienced and conscientiousbuilder may then develop an intuition about the lengths required toachieve a minimum structurally insulative R-value with common buildingmaterials such as wood without any actual measurements or calculations.The very concept of a structurally insulative R-value defined hereinwill help create awareness in the building industry about the problem ofthermal bridging, how to accurately quantify the problem, and how tosolve the problem.

The manufacturable products described herein have specified values ofpath lengths and indirectness built in to achieve any required minimumstructurally insulative R-value and therefore do not require anycalculations. After assembling the products, such as structurallyinsulative studs and plates (embodiments of the invention), into astructurally insulative frame (also an embodiment of the invention)using the same traditional methods as conventional stick framing, thebuilder has structurally insulated the building. After filling theair-sealed structural frame with insulation, the insulation contractorcompletes full insulation of the building against heat. A significantadvantage is that the disclosed thermally and structurally insulativeproducts also work to structurally insulate against sound and firespread.

Non-structural insulative construction elements are generally known.Non-structural insulation has features generally including relativelyhigh resistivity and relatively low density by comparison to thestructural elements. It is problematic when the structural elements usedto construct a structure allow energy in the form of heat, fire,electricity, radiation, sound, and vibration to bypass the insulation.It would be useful to provide sufficient strength to the structuralelement and provide sufficient space for insulation within thestructural element yet reduce the flow of energy through the structuralelements themselves in order to improve the performance of an insulatingbarrier or collection of insulating barriers that incorporate thestructural elements.

A preferred solution to this problem is to design and build astructurally insulative insulatable framework that has (1) sufficientlylong metric paths, i.e. the shortest paths along which heat flowsbetween warmer and colder parts of the structure (insulative aspect),(2) sufficient interior space for insulation (insulatable aspect), (3)sufficiently thick and sufficiently wide structural parts (strengthaspect), (4) balanced ratio of structural insulation length to thicknessof insulation layers (balance between the insulative and insulatableaspects), (5) balanced ratio between thickness of insulation layers andthickness of structural parts (balance between insulatable and strengthaspects).

Although developed for fire-safety and energy-efficiency in residentialand commercial buildings, the present embodiments and methods have abroad range of application in other areas requiring structures thatinsulate not just against heat but also other forms of energy such assound, fire, electricity, and vibration. For example, application of thedisclosed embodiments on a microstructural or nano-structural level,with a sufficiently insulative gas filling the internal cavities,promise materials with high, engineered values of structurallyinsulative resistance and better overall resistance than that ofstate-of-the-art materials.

DISCLOSURE OF THE INVENTION

Bearing in mind the problems and deficiencies of the prior art, it istherefore an object of the present invention to provide a structuralmember which has insulative properties.

It is another object of the present invention to provide a structuralmember which compliment insulative materials used with the structuralmember.

A further object of the invention is to provide a structural member forsupporting panels on opposing sides of the structural member whichresists heat transfer between the opposing panels.

It is yet another object of the present invention to provide a panelstructure having spaced first and second planar panels which providestructural integrity and resistance to heat transfer.

Still other objects and advantages of the invention will in part beobvious and will in part be apparent from the specification.

The above and other objects, which will be apparent to those skilled inthe art, are achieved in the present invention which is directed to apanel structure including spaced first and second planar panels and aplurality of spaced structural members connecting facing surfaces of thefirst and second panels. Each of the structural members includes a firstframe member in contact with the first planar panel in a longitudinaldirection, a second frame member in contact with the second planar panelin the longitudinal direction, the second frame member being spaced fromthe first frame member and substantially parallel thereto and aconnecting frame member between and contacting the first and secondframe members, the connecting frame member contacting the first framemember at a plurality of first locations and contacting the second framemember at a plurality of second locations, the first and second framemembers having free interior-facing surfaces between the first andsecond locations. The connecting frame member provides no direct path ofconductive heat flow, in a direction perpendicular to the longitudinaldirection, between interior-facing surfaces of the first and secondframe members. The structural members may be made of wood or a compositethereof. The distance between first locations and second locations is atleast 2 times the distance between the first and second frame members.The connecting frame member comprises a central frame membersubstantially parallel to the first and second frame members and aplurality of linking members perpendicular to the central frame membersin contact with the first and second frame members at the first andsecond locations. The connecting frame member comprises a central framemember substantially parallel to the first and second frame members anda plurality of first linking members connecting a first surface of thecentral frame member to the first frame member and a plurality of secondlinking members connecting a second surface of the central frame memberopposite the first surface of the central frame member to the secondframe member. None of the first linking members are directly oppositeany of the second linking members. The connecting frame member comprisesa central frame member substantially parallel to the first and secondframe members and a plurality of linking members, each linking membersecured either diagonally between the first frame member and the centralframe member or diagonally between the second frame member and thecentral frame member. The panel structure may include secondary linkingmembers connecting one of the spaced structural members to at least oneother spaced structural member. The secondary linking members mayconnect one of the spaced structural members to at least one otherspaced structural member wherein the secondary linking members provideno direct path of conductive heat flow, in a direction perpendicular tothe longitudinal direction, between spaced structural members.

Another aspect of the present invention is directed to a method ofmaking a panel structure, the plurality of spaced structural membershave the facing surfaces of the first and second panels connected usingthe structural members wherein the connecting frame member provides nodirect path of conductive heat flow, in a direction perpendicular to thelongitudinal direction, between interior-facing surfaces of the firstand second frame members.

Another aspect of the present invention is directed to a structuralmember which connects a first and a second panel to make a panelstructure. The structural member includes a first elongated framemember, a second elongated frame member spaced from and substantiallyparallel to the first elongated frame member and a connecting framemember between and contacting the first and second frame members, theconnecting frame member contacting the first frame member at a pluralityof first locations and contacting the second frame member at a pluralityof second locations, the first and second frame members having freeinterior-facing surfaces between the first and second locations. Theconnecting frame member provides no direct path of conductive heat flow,in a direction perpendicular to the longitudinal direction, betweeninterior-facing surfaces of the first and second frame members.

Another aspect of the present invention is directed to an insulativestructural member including a first elongated frame member having afirst length and a second elongated frame member spaced from andsubstantially parallel to the first elongated frame member, the secondelongated frame member having a second length substantially the same asthe first length. The insulative structural member includes a centralelongated frame member spaced between and parallel to the first andsecond frame members, the central frame member having a third lengthsubstantially the same as the first length and a plurality of firstconnecting members joining the first elongated member to one surface ofthe central frame member, the first connecting members having aconnection length shorter than the first length. The insulativestructural member includes a plurality of second connecting membersjoining the second elongated member to an opposite surface of thecentral frame member, the second connecting members having a connectionlength substantially shorter than the first length. The structuralmember provides no direct path of conductive heat flow, in a directionperpendicular to the first length. The connection length of theplurality of first connecting members and the plurality of secondconnecting members may be less than 20% of the first length of the firstelongated frame member and additionally may be less than 10% of thefirst length of the first elongated frame member. The first, second andcentral elongated members each may comprise a plurality of elongatedlamination members secured to adjacent elongated members, and the firstand second connecting members are comprise a plurality of connectinglamination members. The connecting lamination members of the firstconnecting members may be interwoven with the elongated laminationmembers of the first and central elongated members and the connectinglamination members of the second connecting members are interwoven withthe elongated lamination members of the second and central elongatedmembers. The first and second connecting members may be secureddiagonally between the corresponding first or second elongated framemember and the central frame member. The first and second connectingmembers may be configured to give a first metric path between an outsidesurface of the first elongated frame member an opposing outside surfaceof the second elongated frame member with a first length L1 a first spanS1 a first span-wise indirectness I1={L1/S1}−1 greater than 100%(insulative aspect) equivalent to a first geometrical insulation factorF1=L1/S1 greater than 2, wherein the first metric path is shorter thanany other metric path between the interior and exterior surfaces. Thefirst and second connecting members may be configured to give a firstdirect path between an outside surface of the first elongated framemember an opposing outside surface of the second elongated frame memberwith a second span and a first cumulative distance between structuralparts (a) greater than {(9%±1%) times the second span} (insulatableaspect) and (b) less than {80% times the second span} (not soinsulatable that the structure becomes weak) wherein the firstcumulative distance between structural parts is less than any othercumulative distance between structural parts for any other direct pathbetween the interior and exterior surfaces. The first and secondconnecting members may be configured to give a first path length that isless than 85 times first cumulative distance between structural parts(balance between the insulatable and insulative aspects). wherein thestructural parts include each structural member and the first and secondconnecting member.

Another aspect of the present invention is directed to an insulativestructural panel having a front surface and back surface, the insulativestructural panel comprising a pair of spaced structural members having afirst length, a depth extending between the front surface and backsurface, a width extending perpendicular to the depth, and spaced acrossin a direction of the width. Each spaced structural member comprises afirst elongated frame member positioned along the back surface andextending in the direction of the spaced structural member length, asecond elongated frame member positioned along the front surface spacedfrom and substantially parallel to the first elongated frame member, thesecond elongated frame member having a second length substantially thesame as the first length and a central elongated frame member spacedbetween and parallel to the first and second frame members, the centralframe member having a third length substantially the same as the firstlength. Each spaced structural member comprises a plurality of firstconnecting members joining the first elongated member to one surface ofthe central frame member, the first connecting members having aconnection length shorter than the first length and a plurality ofsecond connecting members joining the second elongated member to anopposite surface of the central frame member, the second connectingmembers having a connection length substantially shorter than the firstlength. The spaced structural member provides no direct path ofconductive heat flow, in a direction perpendicular to the first length.The insulative structural panel includes a hardenable insulativematerial disposed between the front surface and the rear surface in adirection of the depth, between each of the spaced structural members inthe direction of the width and substantially all of the space betweenthe first and second frame members. The insulative structural panel mayinclude at least one additional spaced structural member disposedparallel to the pair of spaced structural members. The insulativestructural panel may include at least one additional spaced structuralmember perpendicular to the pair of spaced structural members. The atleast one additional spaced structural member may be attached at eachend to one of the pair of spaced structural member end. The insulativestructural panel may include a foil radiant barrier attached to at leastone of the front or rear surfaces. The hardenable insulative materialmay be a rigid closed-cell polyurethane foam.

Another aspect of the present invention is directed to an insulativewindow frame for installing a window having a perimeter. The windowframe comprises a plurality of structural members joined around theperimeter of the window. Each structural member comprises a first framemember disposed along an edge of the window on one side of the windowand a second frame member disposed along the edge of the window on theopposite side of the window and spaced from and substantially parallelto the first frame member. Each structural member includes a connectingwindow member between and contacting the first and second frame members,the connecting window member contacting the first frame member at aplurality of first locations and contacting the second frame member at aplurality of second locations, the first and second frame members havingfree interior-facing surfaces between the first and second locations.The connecting window member provides no direct path of conductive heatflow, in a direction perpendicular to the longitudinal direction,between the first and second frame members. The connecting window membermay extend diagonally between the first frame member and the secondframe member. The connecting window member may include a central framemember substantially parallel to the first and second frame members anda plurality of first linking members connecting a first surface of thecentral frame member to the first frame member and a plurality of secondlinking members connecting a second surface of the central frame memberopposite the first surface of the central frame member to the secondframe member.

Another aspect of the present invention is directed to an apparatuscomprising first, second, and third structural members spaced apart fromone another, a first brace connecting the first structural member to thesecond structural member, and a second brace connecting the secondstructural member to the third structural member. The second structuralmember is positioned between the first and third structural members. Thefirst and second braces are configured to give a minimum rangewiseindirectness greater than about zero +5%/−0% for the flow of energyalong the shortest metric path between the first structural member andthird structural member. The first and second braces are configured tomake the cumulative distance between structural members greater than 20%of the apparatus depth.

Another embodiment described herein is an apparatus comprising first,second, and third structural members spaced apart from one another, afirst brace connecting the first structural member to the secondstructural member, and a second brace connecting the second structuralmember to the third structural member. The second structural member ispositioned between the first and third structural members. The first andsecond braces are configured to give a minimum rangewise indirectnessgreater than zero for the flow of energy along metric paths between thefirst structural member and third structural member. This conditionmeans that there are no direct paths and no straight diagonal paths forthe conductive flow of energy through the structural members and braces.

Another aspect of the present invention is directed to a buildingframework, comprising: a first elongated structural member, a secondelongated structural member, and a third elongated structural memberdisposed between the first and second elongated structural members, afirst web member connecting the first and third structural members in aspaced apart relationship, and a second web member connecting the secondand third structural members in a spaced apart relationship, the secondweb member being closer to the first web member than any other webmember disposed between the second and third structural members. Thefirst web member is positioned relative to the second web member suchthat the shortest distance between the first web member and second webmember is greater than or equal 5 times the thickness of the thirdstructural member.

Another aspect of the present invention is directed to a buildingframework, comprising: a first elongated structural member, a secondelongated structural member, and a third elongated structural memberdisposed between the first and second elongated structural members, afirst web member connecting the first and third structural members in aspaced apart relationship, and a second web member connecting the secondand third structural members in a spaced apart relationship. The firstweb member is positioned relative to the second web member such that themost direct metric path between the first elongated structural memberand second elongated structural members establish has a minimumspan-wise indirectness is greater than 100% (structural insulationfactor greater than 2) for the flow of energy between any point on thefirst structural member and any point on the second structural member.

Another aspect of the present invention is directed to a method ofmaking a building framework, comprising: obtaining first, second, andthird structural members, obtaining a first web member configured to bepositioned between the first and third structural members, and a secondweb member configured to be positioned between the second and thirdstructural members, determining connecting locations for the first andsecond web members to ensure the most direct metric through-pathestablishing a maximum span-wise indirectness greater than zero for theflow of energy between any point on the first structural member and anypoint on the second structural member, and connecting the web members tothe structural members at the determined connecting locations.

Another aspect of the present invention is directed to an insulatablebuilding framework comprising: a first elongated structural member and asecond elongated structural member in a coplanar arrangement; a firstweb member connecting the first and second elongated structural members;wherein either the web member is non-linear resulting in a range-wiseindirectness greater than zero for the shortest metric path between thefirst and second structural members, or the web member is straight(linear) and has a slope substantially equal to r1/r2, wherein r1 is athermal resistivity of an insulating material surrounding the web memberand r2 is a thermal resistivity of the web member along its length. Inembodiments, the web member is straight and the angle between the webmember and first elongated structural member is between about 5° andabout 40°. The thermal resisitivity r1 may also be a thermal resistivityof an insulating material surrounding the apparatus which may bedifferent than the insulating material surrounding the web member.

Another aspect of the present invention is directed to a buildingapparatus comprising a set of structural parts, the structural partscomprising a first structural-member (a), a second structural-member(b), a third structural-member, a first web, a first web-member, asecond web, and a second web-member, the second structural-memberpositioned between the first and third structural-members, the first webcomprising the first web-member, the second web comprising the secondweb-member, each web-member in the first web connecting the first andsecond structural-members in a spaced apart relationship at a minimumdistance greater than 30% times the thickness of the secondstructural-member, each web-member in the second web connecting thesecond and third structural-members in a spaced apart relationship, eachweb-member being made of a material with a tensile strength along thestrongest axis of the material greater than about 1% of the leasttensile strength of the structural-members. The structural parts aredimensioned and positioned so as to comprise at least one of (A) a mostdirect through-path through the structural parts at least 1.5 timeslonger than the span of the most direct path through the structuralparts or (B) a most direct path through the structural parts at least 2times longer than the span of the most direct path through thestructural parts or (C) a most direct path through the structural partsat least 2.5 times longer than the span of the most direct path throughthe structural parts or (D) a most direct path through the structuralparts at least 3 times longer than the span of the most direct paththrough the structural parts or (E) a web-member that connects a pair ofstructural-members in a spaced apart relationship at a minimum distancegreater than 30% times the thickness of the second structural-member.

BRIEF DESCRIPTION OF THE DRAWINGS

The features of the invention believed to be novel and the elementscharacteristic of the invention are set forth with particularity in theappended claims. The Fig.s are for illustration purposes only and arenot drawn to scale. The invention itself, however, both as toorganization and method of operation, may best be understood byreference to the detailed description which follows taken in conjunctionwith the accompanying drawings in which:

FIG. 1A illustrates a first embodiment of the framework configuration.

FIG. 1B illustrates the first embodiment of the framework configurationwith insulating substance.

FIG. 1C-1H illustrate energy flow paths through the structural memberand web members of a framework.

FIG. 2AA-2AD illustrates embodiments with diagonal web members.

FIG. 2AE illustrates a control with diagonal web members.

FIG. 2AH illustrates preferred embodiment of a nominal 2×6 stud whichcan be scaled to ascertain preferred embodiments of nominal 2×3, 2×4,N×M where N and M can take on integer values.

FIGS. 2B-2I schematically show various embodiments of 1D and 2D(biaxial) frameworks with more than one layer of diagonal braces.

FIGS. 2M-2T schematically show various embodiments of uniaxial/1Dframeworks with straight braces.

FIGS. 3G-3L show various web member shapes.

FIGS. 4A-4F show various web member shapes in a three chord truss.

FIGS. 5AA-5AF schematically show various web member (spacer orconnector) shapes in the half-unit-cell of a framework with two chords.

FIGS. 5A-5F schematically show various web member shapes in thehalf-unit-cell of a framework with three chords.

FIGS. 6A-6C illustrate embodiments having three chords in one directionand three chords in another direction.

FIGS. 6D-6F illustrate different structurally insulative biaxialframeworks.

FIGS. 6G-6H illustrate structurally insulative, insulatable frameworkswith a bend in them.

FIG. 6I shows a structure that is not itself an embodiment of aninsulatable, insulative framework but is a potential component inembodiments of a biaxial framework.

FIGS. 7-10 each illustrate a combination of a uniaxial framework and aninternetworking web array that each constitute a biaxial framework 6Aand constitute an embodiment of an insulatable, insulative framework.

FIG. 12A shows a triple-pane window comprising first, second, and thirdbiaxial frameworks that are shown and fourth biaxial framework that isnot shown to better illustrate the structure.

FIG. 12B shows the embodiment of FIG. 12A with sheathing.

FIG. 12C shows the opposing view of FIG. 12A.

FIG. 12D shows the opposing view of FIG. 12B.

FIG. 12E shows a frame embodiment incorporating four uniaxialframeworks.

FIG. 12F shows the embodiment of FIG. 12E with one of the four biaxialframeworks removed and additionally comprising six sheets of materialbetween the uniaxial frameworks.

FIG. 12G illustrates the union of four uniaxial frameworks using a firstmethod of joinery.

FIG. 12H illustrates the union of four uniaxial frameworks using asecond method of joinery.

FIG. 12I illustrates the union of four uniaxial frameworks using a thirdmethod of joinery.

FIG. 13A shows structure 800 and demonstrates how uniaxial frameworksand biaxial frameworks can combine to form a frame that structurallyinsulates in three directions.

FIG. 13B shows a close-up view of the south east corner of structure 800shown in FIG. 13A.

FIG. 14 illustrates one embodiment of a cylindrical tube framework.

FIG. 15 illustrates one embodiment of a biaxial framework thatstructurally insulates in the longitudinal direction of the biaxialframework.

FIG. 16 illustrates one embodiment of a triaxial framework with a frontlayer of three strut-like structures and a front layer of fourbrace-like structures.

FIG. 17A illustrates one embodiment of an insulatable, insulativeframework in the form of a building panel including.

FIG. 17B shows the structural members and web members of the buildingpanel of FIG. 17A without the other parts.

FIG. 18 illustrates one embodiment of an insulatable, insulativeframework as a building panel containing a lattice structure between twocoverings.

FIG. 19 illustrates one embodiment of an insulatable, insulativeframework as a triple-pane window with a scarf joint.

FIG. 20A illustrates an embodiment of the framework demonstrating how tomake and use a scarf joint to connect biaxial frameworks together.

FIGS. 20B-20C schematically illustrate various embodiments of theframework depicted in FIG. 20A.

FIG. 21 illustrates one embodiment of the framework that reduces theflow of energy along its normal axis.

FIG. 22A illustrates one embodiment of the uniaxial/1D framework filledwith insulating substance.

FIG. 22B magnifies the dotted-line region of FIG. 22A.

FIGS. 23A and 23B illustrate two types of connections between astructurally insulative stud and a structurally insulative top plate.

FIGS. 24A and 24B illustrate a framework comprising laminations.

FIGS. 25A-25F schematically illustrate different embodiments of ajoist-like framework and views of the framework with and withoutstraight-through, web-member braces.

FIG. 26 illustrates another embodiment of a joist-like framework withstraight through web members.

FIGS. 27A and 27B illustrate another embodiment of the three-chordI-beam containing two closed web-members.

FIG. 28A illustrates one embodiment of the roof framework.

FIG. 28B illustrates the framework in FIG. 28A with gussets to join theframework members together.

FIG. 29 illustrates another embodiment of the framework incorporating aroof truss on an enclosure.

FIGS. 30A-30D schematically illustrate various stacked and rotatedembodiments of the framework with seamless connections of structuralweb-members and braces.

FIGS. 31A-31D schematically illustrate various embodiments of theframework stacked and rotated.

FIGS. 32A-32J schematically illustrate different embodiments of theframework with curves, bends, twists, bulges, and other distortions.

FIG. 33 illustrates one embodiment of the framework in radial form withsurface web-member protrusions.

FIG. 34 depicts one embodiment of the three-chord framework andpotential energy path.

FIGS. 35A-35C depict embodiments of the framework in a rectangular framewith and without insulating substance.

FIG. 36A depicts one embodiment of the framework (left side) adjacent toa conventional stud wall (right side).

FIGS. 36A, 36B show results of thermal imaging in side-by-sidecomparison testing of wall assemblies built with battens andstructurally insulative studs (an embodiment of the invention) versusconventional studs with exteriorly applied rigid foam insulation.

FIGS. 36C, 36D show drawings of a test assembly incorporatingstructurally insulative studs and cross braces (embodiments of theinvention).

FIG. 36F shows results of thermal imaging in a side-by-side comparisontesting of wall assemblies built with structurally insulative studs (anembodiment of the invention) versus conventional studs with exteriorlyapplied rigid foam insulation.

FIG. 36F shows results of thermal imaging in a side-by-side comparisontesting of wall assemblies built with structurally insulative studs (anembodiment of the invention) versus control studs with foam web membersinstead of wood web members.

FIG. 36H shows a thermal photograph of interior surfaces for (1) aprototype window 2963, (2) R-15 (° F.·ft² per BTUh) insulation 2966surrounding the prototype window, and (3) a standard double pane window2960.

FIG. 36I shows a thermal photograph of exterior surfaces for (1) theprototype window 2970, (2) R-15 (° F.·ft² per BTUh) insulation 2973surrounding the prototype window, and (3) a standard double pane window2976.

FIG. 36J shows a thermal photograph like that of FIG. 36I but showing aportion of cold sky 2983 with a temperature of −40° F. and another viewof window 2980 with a different exposure level for the thermal imager.

FIG. 37 depicts one type of joint used between framework structures.

FIG. 38A-38F illustrate different embodiments of uniaxial frameworksjoined together into a biaxial framework.

FIG. 39 shows multiple structurally insulative two chord frameworks.

FIG. 40 shows a metric path through an apparatus with irregularly shapedpassages, cavities, protrusions, edges, and boundaries of the apparatus(shown with black lines).

FIGS. 41A, 41B, 42A, 42B illustrate different four chord uniaxialframeworks with different cross sectional shapes.

FIG. 43 is an exploded perspective view of a panel structure accordingto the present invention.

FIG. 44 is an exploded perspective view of an insulated panel structureaccording to the present invention.

FIG. 45 is a perspective view of a structure member according to thepresent invention.

FIG. 46 is a perspective view of a laminated structure member accordingto the present invention.

The section entitled “Definitions” provides a list of definitions toclarify the meaning of words and terminology used in this application.The remaining paragraphs in this section define terminology used todescribe and illustrate directions in the next section which describesthe figures in detail.

Definitions

The following definitions are generally used in the context of thespecification, but the word used out of context may take the ordinarymeaning.

Unless otherwise specified to the contrary, each of the followingdefinitions holds in the stated context and the context of aninsulatable, insulative framework apparatus. The definitions are givento a first level of approximation and sometimes a second level ofapproximation. In third and higher levels of approximation, one may needto interpret and modify the definitions below using the fullspecification, mathematics, physics, and linguistics in order to makeeverything consistent and error free. Unless otherwise stated all othermeanings of the words and phrases apply outside of the stated context.

1 by 3 (N by M): (in the context of an insulatable insulative framework)the dimensions of the framework expressed as N, the number of uniaxialframeworks constituting the framework, and M, the number of structuralmembers in each of the N uniaxial frameworks.

areal thermal resistance: 1. the temperature difference that resists anygiven heat flux through a material divided by the heat flux; 2.temperature difference per unit heat flux needed to sustain one unit ofheat flux; 3. R-value; 4. R_(ø).

bound path: 1. (in the context of a framework) any path that runs on orwithin the framework and that does not run through any of the cavitiesformed by the framework; 2. (in the context of a structure) a path thatruns on or within the structure but does not run through any of thecavities formed by the structure; 3. (in the context of a structure madeof structural parts) any path that runs through the structural parts ofa structure and only the structural parts of the structure.

bound path of least resistance: (in the context of a specified firststructural part and a specified second structural part of a structure)bound path from the first structural part to the second structural partwith a path resistance wherein the path resistance is less than the pathresistance of any other bound path between the first structural part andsecond structural part; 2. (in the context of a specified first locationand a specified second location on or within a structure) bound pathfrom the first lcoation to the second location with a path resistancewherein the path resistance is less than the path resistance of anyother bound path between the first location and second location.

BTUh: BTU per hour

bundle: 1. (in the context of metric paths for an apparatus) a set ofmetric paths that all run through the same sequence of parts of theapparatus; 2. (in the context of metric paths for an apparatus) a set ofmetric paths that converge to the same point.

compressive strength: 1. (SI units) the compressive force per unit area,measured in metric units of N/m², that a structural element canwithstand without failure or plastic deformation; 2. (Imperial units)the compressive force per unit area, measured in imperial units oflbf/in² (PSI), that a structural element can withstand without failureor plastic deformation.

cumulative distance between structural parts: (in the context of aninsulatable, insulative framework) the running total of distance betweenpairs of structural members intersected by a direct path between theoutermost structural members of the framework.

direct path: 1. (in the context of an insulatable, insulative frameworkapparatus) an unconstrained path of least distance that may run throughany part of the insulatable, insulative framework apparatus includingcavities, material within the cavities, and structural parts; 2. (in thecontext of a path with a specified starting point on or within aninsulatable, insulative framework apparatus) an unconstrained path thatmay run through any part of the insulatable, insulative frameworkapparatus including cavities, material within the cavities, andstructural parts with a value of directness greater than that of anyother path starting at the specified starting point; 3. (in the contextof a path with a specified starting location on or within aninsulatable, insulative framework apparatus) an unconstrained path thatmay run through any part of the insulatable, insulative frameworkapparatus including cavities, material within the cavities, andstructural parts with a value of directness greater than that of anyother path starting at the specified starting location;

direct bound path: (in the context of a path with a specified startinglocation on or within an insulatable, insulative framework apparatus) aconstrained path that runs through the structural parts but not throughthe intervening cavities of the insulatable, insulative frameworkapparatus with a value of directness greater than that of any other pathstarting at the specified starting location;

directness: (in the context of a path with a length and a span) spandivided by the length.

fluxwise resistance (R_(ø)): (in the context of a general description ofareal resistance for different forms of energy) 1. the equivalent of“thermal insulation R-value,” otherwise known as areal resistance, whichquantifies the stimulation per unit energy flux required for a unit ofenergy flux to flow through a barrier; 2. the “thermal insulationR-value” or the temperature difference (ΔT) per unit of heat flux(q^(ø)) required for a unit of heat flux to flow through a barrier, thatis R_(ø)=ΔT/q^(ø) as derived from ΔT=q^(ø)R_(ø) or q^(ø)=ΔT/R_(ø)(Fourier's Law for heat); 3. the “electrical insulation R-value” orsquared voltage (ΔV²) per unit of electrical power (p) required for oneunit of electrical power to flow through a barrier, that is R=ΔV²/p orequivalently R_(ø)=ΔV²/p^(ø)=R/A=or=V/R_(ø) as derived from p=ΔV²/R viap·ø=ø·ΔV²/R and p_(ø)=ΔV²/(R·ø⁻¹) and p^(ø)=ΔV²/R_(ø); 4.R(Pa/(m³/s))=Δp(Pa)/Q where Δp is the pressure difference at either endof a channel and Q=volumetric flow rate of air in m³/s [3]; 5. the“acoustic R-value,”=R_(ø)=D·c/cos(⊖), or the squared sound pressurederived from q^(ø)=p² cos(⊖)/(D c) where q^(ø) is the sound energy flux,p is the sound pressure, ⊖ is the angle between the direction of soundpropagation and the normal to the surface, D is the mass density, and cis the speed of sound in the medium (Fourier's Law for sound).

framework: 1. (in the context of an insulatable, insulative frameworkapparatus) a connected set of two or more structural members and one ormore web members, 2. (in the context of an approximate generaldefinition for a structure) structure comprising joined parts orconglomerated particles and intervening spaces wherein the interveningspaces are detectable at a specified resolution.

heat transfer coefficient: 1. areawise thermal conductance; 2. heat fluxsustained by a temperature difference divided by the temperaturedifference.

horizontal: extrinsic direction x.

indirectness: 1. (in the context of a metric path) spanwise indirectnessand/or rangewise indirectness.

insulatable: 1. (adj. in the context of a framework) providing space(s)for insulation inside the framework; 2. (adj. in the context of astructure) providing space(s) for insulation inside the structure; 3.able to be insulated

insulative axis: (in the context of a framework) any intrinsic directionor intrinsic angle of the framework along which a metric path has a spanand sufficiently large value of rangewise indirectness or spanwiseindirectness.

insulative material: (in the context of this document) any mixture ofsubstances that resists the flow of energy through an apparatus such asclosed-cell insulation, open-cell insulation, rigid insulation,loose-fill insulation, blown-in insulation, spray-applied insulation,batt insulation, foam, expanding foam, spray foam, foamed-in-placeinsulation, cork, mud, straw, waddle/daub, sand, autoclaved aeratedconcrete, wood fiber, wood fiberboard, glass wool, cloth, ceramiccomposites, foils, films, fiber-mat polymers, asbestos, cellular glassboard, cementitious foam, polyisocyanurate foam, polyurethane foam,polystyrene foam, extruded polystyrene foam, expanded polystyrene foam,fiberglass batts, cellulose insulation, aerogel, vermiculite, perlite,mineral wool, natural fibers, cotton, straw, hemp, plastic, wool,atmospheric pressure gas, atmospheric pressure gas with a largermolecular weight than air, low-pressure gas, noble gas, greenhouse gas,thermal insulation, electrical insulation, radiant barrier, acousticinsulation, fire-retardant insulation, fire-proof insulation, etc.

internetworking web member: a connector between first and secondframeworks that is shared by the first and second frameworks (synonym ofexternal web member).

internetworking: (in the context of a web member of a multiaxialinsulatable insulative framework apparatus comprising a pair offrameworks) connecting an adjacent pair of frameworks.

intranetworking web member: a connector between structural memberswithin a framework (synonym of internal web member).

intranetworking: (in the context of a web member of a multiaxialinsulatable insulative framework apparatus) connecting the first andsecond structural members in an adjacent pair of structural members.

isothermal and adiabatic approximation of resistance: See for examplepage 148 [2]. <.See file://Wright-truss-parallel-resistance-formula-derviation-adiabatic-approximation.mw.>

least cumulative thickness of structural parts: the least value ofcumulative length of each successive line segment over which any one ofthe structural parts overlaps a long direct path through the structuralparts as evaluated for a representative set of all long direct pathsthrough the structural parts, (example of a criterion that uses thisdefinition) the least cumulative thickness of structural parts beingless than 85% times the length of the longest direct path through thestructural parts,

least resistant bound path: See bound path of least resistance.

length-to-span ratio: 1. (in the context of a path with a span and alength) the length divided by the span of the path; 2. (in the contextof a path with a span and a length) the fractional number of spanscontained in the length; 3. (in the context of resistance) the factor bywhich a spanwise path resistance is multiplied in order to obtain thelengthwise path resistance.

length: 1. (in the context of a path) the length measured along thepath; 2. (in the context of a path) the length measured along the pathand not the range; 3. (in the context of a path) path length.

lengthwise path resistance: See structurally insulative resistance.

long direct path: a direct path that is longer than any other directpath that the direct path overlaps.

longest minor metric path: (in the context of a set of metric pathswithin a bundle) metric path with a length such that the length isgreater than that of any other metric path in the bundle starting at anypoint on the opposite side of the most direct metric path relative tothe start point of the longest metric path; (in the context of a set ofmetric paths) metric path with a length such that the length is greaterthan that of any other metric path starting at any point on the oppositeside of the most direct metric path relative to the start point of thelongest metric path.

longest metric path: (in the context of a set of metric paths within abundle) a metric path with a length such that the length is greater thanthat of any other metric path in the bundle; (in the context of a set ofmetric paths) a metric path with a length such that the length isgreater than that of any other metric path.

maximum rangewise indirectness: the maximum value of the rangewiseindirectness for a specified set of metric paths.

maximum rangewise indirectness: the maximum value of the rangewiseindirectness for the metric paths that run between any first point in afirst specified space to any second point in a second specified space.

maximum rangewise indirectness: 1. (in the context of specified firstand second spaces) maximum value of the rangewise indirectness formetric paths that run between any first point in the first space to anysecond point in the second space; 2. (in the context of a specified setof metric paths) maximum value of the rangewise indirectness for thespecified set of metric paths; 3. (in the context of a most directmetric path) maximum value of rangewise indirectness for the shortestmetric path that overlaps the most direct metric path member: one of aset, group, array, matrix, combination, pair, triplet, multiplet, tuple,or any other collection of things.

metric distance: 1. (as defined inhttps://en.wikipedia.org/wiki/Metric_space#Definition) for any system ofroads and terrain is the distance between two locations can be definedas the length of the shortest route connecting those locations; 2. (inthe context of a metric path in a framework) the length of the shortestmetric path connecting two parts of the framework; 3. (in the context ofa metric path in a structure) the length of the shortest metric pathconnecting two parts of the structure.

metric path: 1. (in the context of a first part of a framework and asecond part of the framework) the shortest path between the first partand second part of the framework; 2. (in the context of a first part ofa framework and a second part of the framework wherein the framework hastemporary web members and/or non-structural web members) the shortestpath between the first part and second part of the framework determinedby excluding temporary web members and non-structural web members; 3.(provisional patent application) the shortest trajectory along whichenergy can flow through an object between any two specified points on orwithin the object; 4. (in the context of a framework made of anisotropically resistive material) bound path of least resistance; 5. (inthe context of a framework made of an isotropically resistive material)least resistant bound path.

metric: (in the context of paths) relating to a binary function of atopological space that gives, for any two points in the space, a valueequal to the distance between them, or equal to a value, treated asanalogous to distance for the purpose of analysis, such as the metricdistance.

minimum rangewise indirectness: the minimum value of the rangewiseindirectness for the metric paths that run between any first point in afirst space to any second point in a second space.

minimum rangewise indirectness: 1. (in the context of specified firstand second spaces) minimum value of the rangewise indirectness formetric paths that run between any first point in the first space to anysecond point in the second space; 2. (in the context of a specified setof metric paths) minimum value of the rangewise indirectness for thespecified set of metric paths; 3. (in the context of a most directmetric path) minimum value of rangewise indirectness for the shortestmetric path that overlaps the most direct metric path.

most direct bound path: (in the context of a first part and second partof a framework) bound path from the first structural part to the secondstructural part characterized by a path length L, a span S, and adirectness S/L, wherein the directness is greater than that of any otherbound path between the first part and second part.

most direct path: (in the context of a path) a direct path possessing agreater value of directness than any other direct path that the directpath overlaps.

most-direct: 1. (in the context of a path) having the least value ofspanwise indirectness; 2. (in the context of a path) having the greatestvalue of directness mother-web: the collection of structural parts thatconnect the outermost structural members in a uniaxial framework.

mother-web-minimum-span: (in the context of Claim 1) the statisticalminimum value of span for the direct-path-set that intersects themother-web.

number: 1. (in the context of the text “any number of” used in claims)any non-negative integer; 2. (in the context of the text “any number of”used in claims) any integer equal to zero or greater than zero.

panel: (in the context of a structure with metric paths and bundles) aspatial region of the structure that contains a single bundle of metricpaths.

part: 1. (in the context of a framework) a structural member, a web, aweb member, a web formation, a structural formation, a node, a surface,a cross-sectional slice, etc. within the framework; 2. (in the contextof a structure) a structural member, a web, a web member, a webformation, a structural formation, a node, a surface, a cross-sectionalslice, etc. within the structure.

path length: (in the context of a metric path with end points) thedistance along a metric path between the end points determined bydividing the metric path into a representative set of path segments andcumulatively summing the segment length of all path segments in therepresentative set of path segments.

path of least resistance: (in the context of a specified first part ofan apparatus and a specified second part of the apparatus) path from thefirst part through any part of the apparatus to the second part with apath resistance wherein the path resistance is less than the pathresistance of any other path.

path resistance: (in the context of a path) local resistivity along thedirection of the path multiplied by the differential length element andintegrated over all differential length elements along the total lengthof the path.

path segment: (in the context of a metric path) part of the metric pathcreated by dividing the metric path into a finite number of pieces, eachsmall enough to qualify as a straight line within the required accuracyfor any given calculation.

r-value: 1. resistivity with overall units of (K m)/W or (°F.·ft)/(BTUh); 2. “small r” value.

range: (in the context of a path with two endpoints) the distancebetween the two endpoints of the path.

range-wise: rangewise.

rangewise directness: (in the context of a path with a path length and arange) range divided by path length.

rangewise indirectness: (in the context of a path with a path length anda range) 1. {path length divided by the range} minus one; 2. (in thecontext of a most direct metric path for a framework) {metric subpathlength divided by metric subpath range} minus one wherein the metricsubpath is the shortest subpath between the outermost structural memberstouched by the most direct metric path; 3. (in the context of a mostdirect metric through-path for a framework) {metric subpath lengthdivided by metric subpath range} minus one wherein the metric subpath isthe shortest subpath between the outermost structural members touched bythe most direct metric through-path.

rangewise number of switchbacks: the number of inflection points along ametric path divided by the range of the metric path rangewise number ofswitchbacks: the number of inflection points along a metric path dividedby the range of the metric path.

rangewise path resistance: 1. (in the context of a path with a rangethrough a material with an isotropic resistivity) the range of the pathmultiplied by the isotropic resistivity of the material; 2. (in thecontext of a path with a length and range through a material with annon-isotropic resistivity described by a resistivity tensor) an integralof the component of the differential length element in the rangewisedirection of the differential length element multiplied by the componentof the resistivity tensor in the rangewise direction of the differentiallength element obtained by integrating over the entire length of thepath.

removable: (in the context of a removable web-member) a web-member thatis non-essential to the structural integrity of a framework that can becompletely removed, and by extension partially removed, so as toeliminate all metric-paths that run through the web-member.

representative set: 1. a subset with a large enough number of elementsto achieve any required level of confidence for a calculation thatdepends on the number of elements in the subset such that the subsetfairly represents the properties of a set that contains the subset; 2. asubset with properties that fairly represents the properties of a setthat contains the subset when subjected to analysis.

resistance: (in the context of this document unless noted otherwise)areal resistance resistivity: 1. temperature gradient per unit of heatflux that sustains one unit of heat flux between a warmer surface andcolder surface of a thermal barrier; (2) (in the context of imperialunits and colloquial expression) R-value per inch; (3) (in the contextof metric units and colloquial expression) R_(SI) per m or R_(SI) permm; (4) (in the context of a general description for all forms ofenergy) the positive stimulation gradient per unit of energy flux thatsustains one unit of energy flux between the higher-stimulation surfaceand lower-stimulation surface of an energy barrier.

resistivity multiplier: See structural insulation factor.

R_(sval): (uppercase “R” subscript “sval”) structurally insulativeresistance.

r_(sval): (lowercase “r” subscript “sval”) structurally insulativeresistivity.

segment length: the distance, as determined using the distance formula,between the end points of a path segment short enough to accuratelyapproximate as a straight line, justify use of the distance formula, andachieve any required accuracy for any calculation that depends thereon.

segment resistance: (in the context of a path segment with a length andspan through a material with an non-isotropic resistivity) segmentlength of the path segment multiplied by the resistivity of the materialin the direction of the path segement.

segment span: (in the context of a metric path with a first end pointand a second end point on or within two specified features) theprojected length of a path segment when projected onto any intersectingline of closest approach, between the two specified features, eachcontaining an end point for the metric path or connecting to anotherfeature that contains an end point for the metric path.

shortest bound path: 1. (in the context of a first part and second partof a framework) any bound path from the first structural part to thesecond structural part characterized by a path length, wherein the pathlength is leess than that of any other bound path between the first partand second part; 2. (in the context of a set of metric paths within abundle) a metric path with a length such that the length is less thanthat of any other metric path in the bundle; 3. (in the context of a setof metric paths) a metric path with a length such that the length isless than that of any other metric path in the set of metric paths.

span-wise directness: (in the context of a metric path with a span andpath length) span divided by path length.

span: (in the context of a metric path with a first end point on a firstsurface and a second end point on a second surface) shortest distancebetween the first and second surfaces as measured from the first endpoint or second end point when the two measurements give the same resultwherein the first and second surfaces may be defined by contours ofconstant depth when either the first end point or second end point arenot on a surface; 2. (in the context of a metric path with a first endpoint on a first surface and a second end point on a second surface) thedistance spanned by a metric path between the first end point and thesecond end point determined by dividing the metric path into arepresentative set of path segments and then cumulatively summing thesegment span for all path segments in the representative set of pathsegments wherein the first and second surfaces may be defined bycontours of constant depth when either the first end point or second endpoint are not on a surface.

span-wise: spanwise.

spanwise direction: (in the context of a path between with twoendpoints) the radius of an osculating.

spanwise indirectness: 1. (in the context of a path with a span and apath length) {path length divided by the span} minus one; 2. (in thecontext of a path with a span and a super-span length) {super-spanlength divided by the span} minus one; 3. (in the context of a path witha span and a length) length-to-span ratio minus one; 5. (in the contextof a path with a spanwise path resistance through an isotropicallyresistive material) factor by which the spanwise path resistance ismultiplied in order to obtain the super-span path resistance of thepath; 6. (in the context of improving resistance for a structure) amultiplicative factor that quantifies the improvement in resistance fora metric path in the structure by comparison to a direct path through asolid of the same material and exterior dimensions as the structure.

spanwise number of switchbacks: the number of inflection points along ametric path divided by the span of the metric path.

spanwise path resistance: 1. (in the context of a path with a spanthrough a material with an isotropic resistivity) the span of the pathmultiplied by the isotropic resistivity of the material; 2. (in thecontext of a path with a length and span through a material with annon-isotropic resistivity described by a resistivity tensor) theresistance along the span of a path determined by dividing the metricpath into a representative set of path segments and then cumulativelysumming the spanwise segment resistance for all path segments in therepresentative set of path segments.

spanwise resistance: spanwise path resistance.

spanwise segment resistance: (in the context of a path segment with alength and span through a material with an non-isotropic resistivity)segment span of the path segment multiplied by the resistivity of thematerial in the spanwise direction of the path segement.

spanresistive indirectness: (in the context of a path with a length anda span) {the path resistance divided by the spanwise path resistance}minus one.

statistical uniformity: first statistic divided by a second statisticwherein the first statistic is the minimum value for a set of values andthe second statistic is the maximum value for the set of values.

stimulation: 1. (in the context of thermal energy) temperature; 2. (inthe context of electrical energy) voltage for electrical energy; 3. (inthe context of acoustical energy) pressure; 4. (in the context ofvibrational energy) pressure; 5. (in the context of mechanical energy)work; 6. (in the context of a general description for all forms ofenergy) quantity analogous to temperature in Fourier's law for allfundamental equations that can be expressed in the same form asFourier's law; 2. temperature for heat flux grad(T)=q^(ø)R_(ø) asderived from q^(ø)=grad(T)/R_(ø) (Fourier's Law for heat); 3. squaredvoltage or voltage for electrical power based on choice of R_(ø)=R_(ø)′or R_(ø)=V/R_(ø)′, ΔV²=p^(ø)R_(ø) as derived from p^(ø)=ΔV²/R_(ø)(Analogy of Fourier's Law for electricity). Note: I think that thesquared voltage will actually be the square of the voltage gradient(grad·V·grad·V) which is the magnitude of the electric field; 4. Squareof sound pressure for acoustic power; 5. pressure for hydraulic power;6. work for mechanical power. 7. the spatial concentration of energyparticles that causes the energy particles to redistribute; 8. Level ofenergetic activity as function of spatial-temporal coordinates.

structural insulation factor: (in the context of a framework with a mostdirect metric path with a length L and span S) L/S.

structural member: 1. a structural part with the primary purpose ofbearing applied structural loads; 2. a primary member of a structure,such as but not limited to a wall, wall frame, stud, portion of a stud,fabric warp, window frame, portion of a window frame, rafter, portion ofa rafter, joist, portion of a joist, chord, portion of a chord; 3. (inthe context of an insulatable insulative framework apparatus withexactly two structural members and exactly one web-member) a structuralpart that interfaces with a web member; 5. (in the context of aninsulatable insulative framework apparatus that conforms to definition 1or 2) a set of any number of structural-sub-members that each physicallytouch one other structural-sub-member in the set; 6. (in the context ofthe claims) a framework.

structural part: (in the context of an insulatable, insulative frameworkapparatus) a part that partially or fully constitutes the framework,possesses significant structural strength relative to other parts of theapparatus, and significantly contributes to the structural strength ofthe framework.

structural strength: 1. (SI units) the force per unit area, measured inmetric units of N/m², that a structural element can withstand withoutfailure or plastic deformation; 2. (Imperial units) the force per unitarea, measured in imperial units of lbf/in² (PSI), that a structuralelement can withstand without failure or plastic deformation.

structural: (in the context of an approximate definition for thisapplication) relating to or forming part of the structure of a buildingor other item, such as a panel, window, window frame, door frame, etc.the structural members of a window frame are not necessarily structuralmembers for a building into which the window frame installs. Thus,“structural” is a relative term that depends on context.

structural: relating to or forming part of the structure of a buildingor other item, such as a panel, window, window frame, door frame, etc.The structural members of a window frame are not necessarily structuralmembers for a building into which the window frame installs. Thus,“structural” is a relative term that depends on context.

structural: serving to form a structure. The term “structural” dependson context. A structural member of a window will not require the samestrength as a structural member for a load bearing wall in a house.

structurally insulate: 1. (in the context of a framework with a mostdirect metric path with a length L and span S) possess a metric pathwith a length that is longer than its span; 2. (in the context ofstructural parts with an isotropic resistivity) possess a path of leastresistance with a span and a structurally insulating resistance forwhich the structurally insulating resistance is greater than theresisitivity multiplied by the span; 3. (in the context of structuralparts with an nonisotropic resistivity) possess a path of leastresistance with a span and a structurally insulating resistance forwhich the structurally insulating resistance is greater than thespanwise resistance.

structurally insulate: 1. (in the context of a specified direction)resist the flow of energy along metric paths with a spanwise directionthat significantly coincides with the specified direction; 2. (in thecontext of an insulatable insulative framework) resist the flow ofenergy along metric paths such as the most direct metric path throughthe framework.

structurally insulative resistance: 1. (in the context of a path with aspan through a material with an isotropic resistivity) the path lengthof the path multiplied by the isotropic resistivity of the material; 2.(in the context of a path with a span through a material with annon-isotropic resistivity) resistance along the length of a pathdetermined by dividing the metric path into a representative set of pathsegments and then cumulatively summing the segment resistance for allpath segments in the representative set of path segments; 3. lengthwisepath resistance; 4. R_(sval).

structurally insulative resistivity: 1. (in the context of a path with aspan through a material with a non-isotropic resistivity) structurallyinsulative resistance of the path divided by spanwise resistance of thepath; 2. (in the context of a path with a span through a material withan isotropic resistivity) structurally insulative resistance of the pathdivided by spanwise resistance of the path; 4. r_(sval).

structurally insulative R-value: 1. (in the context of a metric pathwith a path length through a material with a isototropic resistivity)structurally insulative resistance.

structure: a single body of material with cavities, such as a 3D printedhouse frame or means an object formed from parts such as a framework,frame, window frame, door frame, window, door, building, house, frame ofa building, frame of a house, framework, a lattice, a truss, skyscraper,furniture, etc.

strut: (in the context of U.S. Provisional Patent Application No.62/720,808) chord or an elongate structural member.

subpath length: (in the context of a subpath) arclength along thesubpath.

super-range length: 1. (in the context of a path with a range and alength) the length minus the range; 2. (in the context of a path with arange and a length) the portion of the length that is above and beyondthe range.

super-range resistance: (in the context of a path with a range and alength) the difference between the lengthwise path resistance andrangewise path resistance.

super-span length: 1. (in the context of a path with a span and alength) the length minus the span; 2. (in the context of a path with aspan and a length) the portion of the length that is above and beyondthe span.

super-span resistance: (in the context of a path with a span and alength) the difference between the lengthwise path resistance andspanwise path resistance.

tangential direction: (in the context of an insulatable, insulativeframework apparatus) a term for the longitudinal direction of aframework that curves and loops back on itself to form a ring orring-like structure.

temperature gradient: 1. (simple definition) the difference intemperature across a distance divided by the distance; 2. (physicsdefinition) the vector derivative of a spatial temperature distributionfunction; 3. (in the context of this document) a placeholder forstimulation gradient which might otherwise be considered an indefiniteterm.

temperature: 1. (simple definition) level of thermal activity; 2. (broaddefinition which applies to any form of energy not just thermal energy)level of stimulation; 3. acoustic stimulation.

tensile strength: 1. (SI units) the tensile force per unit area,measured in metric units of N/m², that a structural element canwithstand without failure or plastic deformation; 2. (Imperial units)the tensile force per unit area, measured in imperial units of lbf/in²(PSI), that a structural element can withstand without failure orplastic deformation.

thermal areawise resistance: thermal resistance.

thermal conductance: 1. reciprocal of thermal resistance.

thermal conductance: heat flowrate sustained by a temperature differencedivided by the temperature difference.

thermal conductivity: heat flux sustained by a temperature gradientdivided by the temperature gradient.

thermal conductivity: the thermal gradientwise flux through a material,i. e., the thermal flux through a material in W/m² or BTUh/ft² generatedin proportion to a specified thermal gradient across the material in K/mor ° F./inch with overall units of W/(m K) or (BTUh inch)/(ft²° F.) orBTUh/(ft ° F.) and called the thermal conductivity for short.

thermal energy flux: 1. the energy per unit area per unit timecharacterizing the steady state number of quanta passing through theunit area in unit time. 2. the instantaneous energy per unit area perunit time characterizing the instantaneous number of quanta passingthrough the unit area in unit time.

thermal insulance: 1. the R-value of the material with overall units of(K m²)/W or (° F. ft²)/(BTUh); 2. (in terms of thermal resistance) theapparent areal thermal resistance of a material including the effects ofconduction, convection, and radiation; 3. the reciprocal of thermaltransmittance; 4. the thermally-transmitted-flux-area-wise temperaturedifference across a material.

thermal resistance: temperature difference per unit of heat flow rate.

thermal resistance: 1. the thermal-conductive-flux-wise temperaturedifference across a material; 2. The temperature difference betweenopposing sides of a material in K or ° F. needed to generate a specifiedthermal flux through the material in W/m² or BTUh/ft² with overall unitsof (K m²)/W or (° F. ft²)/(BTUh); 3. a term used in ISO 8497:1994(E),for example; 4. a more exact term for a physical quantity that issometimes called thermal resistance for short [1]; 5. a quantity similarto the R-value of a material except that it only includes the effect ofconduction unlike the R-value which accounts for all modes of heattransfer including radiation and convection as well as conduction; 6.(in terms of thermal insulance) the portion of areawise thermalinsulance associated with heat conduction and no other heat-transfermode; 7. (in terms of R-value) the areawise R-value when conduction isthe only heat-transfer mode.

thermal resistivity: 1. the temperature gradient per unit of heat fluxthat sustains one unit of heat flux between the warmer surface andcolder surface of a barrier; 2. r_(val).

thermal resistivity: ratio of temperature gradient (in K/m or ° F./inch)across an object divided by the conductive heat flux (in W/m² orBTUh/ft²) through the material generated by the thermal gradient withoverall units of (K/m)/(W/m²) or (K·m)/W or (° F. ft²)/(inch BTUh) or(ft ° F.)/BTUh.

through-path: 1. (in the context of a framework comprising structuralmembers and an outermost pair of structural members) path betweenexterior facing sufaces of the outermost pair of structural members ofthe framework; 2. thrupath.

U-value: the thermal transmittance with overall units of W/(m² K) orBTUh/(ft²° F.).

vertical: extrinsic direction y.

web member: 1. (in the context of an insulatable, insulative frameworkapparatus) a structural part with the primary purpose of connectingother structural parts together; 2. (in the context of an insulatable,insulative framework apparatus) a connecting member; 3. (in the contextof a multiaxial framework) an internetworking web member or anintranetworking web member; 4. (in the context of a web as definedherein) a member of the web.

web-members: 1. (in the context of U.S. Provisional Patent ApplicationNo. 62/720,808) webs where “webs” means “web members” in commonparlance; 2. (in the present application) parts of a web where “web”means “collection of web members.”

web: (in the context of an insulatable, insulative framework apparatus)an array of one or more connecting members.

wood product: wood, finger-jointed lumber, variable-length lumber,lumber, logs, timber, paper, cardboard, corrugated cardboard, wood-fiberreinforced plastic, wood-fiber reinforced polymer, fiber board, GUTEX,medium density fiberboard (MDF), high-density fiberboard (HDF), orientedstrand board, plywood, artificial wood, engineered lumber, structuralcomposite lumber (SCL), laminated veneer lumber (LVL), cross laminatedtimber (CLT), cross-laminated lumber (CLL), dowel-laminated timber(DLT), dowel laminated lumber (DLL), toothpicks, nail laminated timber(NLT), nail-laminated lumber NLL), parallam, glulam, engineered strandlumber (ESL), laminated strand lumber (LSL), oriented strand lumber(OSL), parallel strand lumber (PSL), other forms of structural compositelumber, other forms of engineered lumber, other engineered woodproducts.

MODE(S) FOR CARRYING OUT INVENTION

In describing the embodiments of the present invention, reference willbe made herein to FIGS. 1-46 of the drawings in which like numeralsrefer to like features of the invention.

In a first embodiment of the present invention, a plurality ofweb-members or web-member-like structures are disposed between andjoining together a plurality of structural members orstructural-member-like structures to form a labyrinth of passages withintervening cavities. The cavities are preferably filled with one ormore than one insulative filler substance or an embodiment of thedisclosed apparatus to reduce the flow of energy through the cavities.In some embodiments, no insulative filler substance is used. In someembodiments, the cavities are evacuated to create a vacuum with aresidual partial pressure of any magnitude. The passages and cavitiespreferably have shapes and proportions such that the shortest paths,through the passages between different parts of the apparatus, have asufficiently long length in proportion to their span or range to createa multiplicative gain in resistance to the throughput of energy alongtargeted axes of the apparatus. Any gain in resistance relative to thatof a direct-path provides a means to reduce the flow of energy throughthe apparatus even when made with structural materials that bycomparison to the insulative filler substance generally have a higherdensity and lower resistivity. The cavities preferably have a geometrythat balances the set of goals comprising (1) minimizing any reductionin strength of the apparatus, (2) creating space for one or more thanone insulative filler substance, (3) maximizing the length of metricpaths through the apparatus, (4) reducing transfer of the targeted formsof energy along direct paths through the apparatus and (5) reducingtransfer of the targeted forms of energy along any path through theapparatus. The relative importance of each goal depends on theparticular application. Thus, the relative importance of each goalpreferably factors into the design and engineering of any givenapparatus for any particular application.

When designing and engineering an apparatus, one should take care toproperly assess the resistivity for the targeted forms of energy of thematerials used to make the structural members and web members.Resistivity for all forms of energy is generally described by a tensorwith different components that depend on the direction of energy flowrelative to the axes of the material, that depend on the internalstructure of the material. One should also take care to properly assessthe strength of the materials used to make the structural members andweb members. Strength is also generally described by a tensor withdifferent components that depend on the orientation of the axes of thematerial relative to applied force. For instance wood and othermaterials containing fibers have strength, conductivity, and resistivityvalues that depend on orientation of the fibers relative to stimuli. Thestrength along the fibers is greater than the strength perpendicular tothe fibers. The conductivity along the fibers is also greater than theconductivity perpendicular to the fibers. The resistivity along thefibers is less than the resistivity perpendicular to the fibers.Additional benefits of the disclosed apparatus may include (1) increasedsurface area for greater capacitance and contact resistance, (2) areduction in area through which energy can flow, (3) an increase indimensional stability, (4) a reduction in weight, (5) directingmechanical forces to flow along the strong axis of employed structuralmaterials, (6) providing space for installation of fasteners, forexample nuts, bolts, floating tenons, rivets, and clinched nails, andother fasteners that require space for installation, (7) reducing theneed to drill holes through framing members for installation ofutilities, (8) providing space to run structural bracing, structuralreinforcement cables, and tie-down cables, (9) reducing the moment armon web-members under tension and compression, (10) reduction in laborcosts, material costs, injury costs, and overall cost for constructionof insulated buildings, (11) reduction in cost of manufacturing anddistribution of insulative materials, (12) greater energy efficiency,(13) similar or higher strength, or (14) higher strength to weight ratiorelative to a similar size structural element that has no cavities,smaller cavities, or inferior geometry.

Furthermore, the disclosed means of reducing energy transfer canpreserve or even increase the cross sectional area of the passages yetstill reduce energy transfer through the passages. For instance anembodiment of the apparatus can have arbitrarily large lateral dimensionto achieve a targeted structural strength without compromising thethermal performance of the apparatus along its normal axis. Anembodiment of the disclosed apparatus also enables the reduction ofenergy transfer along two, three, or any number of its axes calledinsulative axes. Embodiments can insulate even when web members andstructural members are made from the same structural material orstructural materials with similar values of resistivity. Embodiments cancompensate for situations in which web-members, for reasons ofstructural integrity, economic cost or other practical concerns, areoriented such that the least resistive axis aligns with the path ofenergy flow through the structure in an undesirable direction. Thematerial constituting the web members, do not need a significantlyhigher resistivity than the structural members. An embodiment canstructurally insulate even when the structure constitutes a thermallyunbroken framework for which the resistivity of web members is less thanor equal to the resistivity of the structural members along the path ofundesirable energy flow. Different embodiments of the disclosedapparatus may reduce the transmission of different forms of energy suchas heat, sound, vibration, shock waves, electricity, electromagneticenergy, radiation, and fire. Thus, embodiments of the apparatus areuseful for energy efficiency, temperature regulation, harnessing naturalpower sources, temperature control, construction, material science,energy storage, and numerous other applications. Corresponding usage,systems, and methods also are disclosed. Generally, the disclosedmethods can be applied to improve the insulative value of an arbitrarystructural frame or material, for instance through the selective removalof material or creating frameworks to engineer indirect metric-paths andproperly size cavities within frameworks.

Statistical functions can be used to characterize propertiescharacterizing the set of metric paths for different embodiments of thedisclosed apparatuses. Spanwise indirectness, rangewise indirectness,structural insulation factor, rangewise indirectness multiplier,spanwise number of switchbacks, rangewise number of switchbacks,planarity of spanwise indirectness, and planarity of rangewiseindirectness, are all examples of properties that characterize the setof metric paths for different embodiments of the disclosed apparatuses.Normalized spread, statistical uniformity, average, standard deviation,average deviation, maximum, minimum, statistical range, variance, areall statistical functions that may be applied to the properties thatcharacterize the set of metric paths for different embodiments of thedisclosed apparatuses. I anticipate use of these properties andstatistical functions to further define the scope of the disclosedinvention in future patent applications.

In FIGS. 1A and 1B and in general, any particular framework has threeintrinsic directions,

(lateral),

(longitudinal),

(normal). Intrinsic direction

, the longitudinal direction, runs parallel to the length of theframework. Intrinsic direction

, the normal direction, runs perpendicularly relative to thelongitudinal direction and parallel to a line that runs through thecenter of the first, second and third chords. Intrinsic direction

, the lateral direction, runs perpendicular to the normal direction andlongitudinal directions. Each intrinsic direction has an associated axisthat runs through the center of gravity by convention in thisapplication unless otherwise specified. These directions apply generallyto any object. If an object is part of a framework apparatus then thelongitudinal direction

of the part corresponds to the lengthwise direction of the part. Whenthe object is not elongated in any direction, then the longitudinaldirection corresponds to that of the framework that comprises the partunless otherwise specified. When any particular intrinsic direction ofan object is ambiguous, then the intrinsic direction corresponds to thatof the framework that comprises the part unless otherwise specified.

The words “horizontal,” “vertical,” and “transverse” are associated withextrinsic directions x, y, z, respectively. The extrinsic directions maybe indicated in a figure with three line segments labeled x, y, z thatemanate from a single point. The line segment labeled with an xindicates the positive/negative horizontal direction which are sometimereferred to as right/left. The line segment labeled with an y indicatesthe positive/negative vertical direction which are sometimes referred toas up/down. The line segment labeled with an z indicates the positiveand negative vertical direction which are sometimes described as “intothe page” and “out of the page,” respectively. The words “horizontal,”“vertical,” and “transverse” do not refer to the intrinsic axes of theframeworks and do not limit their use. If no other indication exists tothe contrary, then, when the text is right side up, (a) the verticaldirection runs parallel to the long axis of a figure page and definesthe terms up and down, (b) the horizontal direction runs parallel to theshort axis of the figure page defining the terms left and right, and (c)the transverse direction runs into and out of the page defining theterms inward and outward. In the absence of further detail, thelongitudinal direction of a reference object is associated with theextrinsic directional adjective used to describe it. For example“horizontal framework 10” in reference to FIG. 1A would indicate thatthe horizontal direction runs parallel to the longitudinal axis offramework 10.

The three intrinsic directions x, y, z define intrinsic orbitaldirections O

, O

, O

. Each intrinsic orbital direction O

, O

, O

characterizes an orbital rotation around an intrinsic direction of anyparticular framework or object where the axis of rotation does notcoincide with the axis for the particular intrinsic direction. Intrinsicangle O

, the orbital roll angle, characterizes rotations around thelongitudinal direction when the orbital roll axis and longitudinal axisare displaced as in a spiraling movement. Intrinsic angle O

, the orbital yaw angle, characterizes rotations around the normaldirection when the rotational yaw axis and normal axis are displaced asin a turn made by a car. Intrinsic angle O

, the orbital pitch angle, characterizes rotations around the lateraldirection when the orbital pitch axis and lateral axis are displaced asin a loop-the-loop movement. Each intrinsic orbital direction can beused to define positions, offsets, and differences in angle. When theaxis of rotation around an intrinsic direction does coincide with therotational axis for an intrinsic orbital direction, then the orbitalrotation becomes a pure rotation called a spin. In that case each of thethree intrinsic angles O

, O

, O

characterize a spin rotation around an intrinsic direction of anyparticular framework or object because the rotational axis coincideswith that of the intrinsic direction. To distinguish between orbitalangles and spin angles, a slash is added to the symbol for spin angles.Intrinsic spin angle Ø

, called the roll angle, characterizes spin rotations around thelongitudinal direction when the orbital roll axis and longitudinal axiscoincide. Intrinsic spin angle Ø

, the orbital yaw angle, characterizes rotations around the normaldirection when the rotational yaw axis and normal axis coincide.Intrinsic spin angle Ø

, the pitch angle, characterizes rotations around the lateral directionwhen the orbital pitch axis and lateral axis coincide. Each of theextrinsic directions x, y, z define extrinsic orbital angles Ox, O̧y, Ozand extrinsic spin angles Øx, Øy, Øz. The extrinsic orbital angles Ox,Oy, Oz apply to orbital rotation of an object around an axis parallel toan extrinsic direction that does not intersect the object. The extrinsicspin angles Øx, Øy, Øz apply to the spin rotation of an object around anaxis parallel to an extrinsic direction that does intersect the object.Pure spin rotation of an object occurs when the rotational axiscoincides with the axis of the associated extrinsic or intrinsicdirection. The central axis of any orbital/spin angle can be inferred byfinding the center of a circle that overlaps the arc drawn in a figureto indicate the orbital/spin angle. Each orbital angle and spin angle isalso useful for describing angular position, offset and differences inangular position.

Each embodiment also has related embodiments based on the orientation ofmaterials constituting the framework. The orientation of a materialwithin a structural member, web-member, or any part of a frameworkapparatus is important when the material has non-isotropic strengthproperties. The present specification uses the arbitrary convention thatY indicates the direction of greatest strength for a material, Xindicates the direction of least strength, and Z indicates the directiontransverse to the X and Y directions. In the case of a wood structuralmember the direction of greatest material strength often runs parallelto the longitudinal direction of the structural member. Material orbitalangles O _(X) , O _(Y) , O _(Z) and material spin angles Ø _(X) , Ø _(Y), Ø _(Z) can also be defined for the linear material directions X, Y, Z.

A label containing X, Y, Z, x, y, z,

,

, or

, followed by a subscripted identification number indicates that thedirection applies to an object labeled with the same identificationnumber in a figure. Such a label is often accompanied by a line or arrowto visually indicate the direction. For example, the arrow labeled Y 104in FIG. 3A indicates the chosen direction of greatest material strengthfor the diagonal web-member 104. Unless explicitly specified theillustrated or described orientation of materials is not limiting. Thearrow labeled Y 105 in FIG. 3G shows that the preferred direction ofgreatest material strength for web-member 105 runs in the same directionas the longitudinal direction of the web-member 105 indicated by thearrow

105. Unless explicitly noted otherwise, any indication of a materialdirection in a figure constitutes a preferred embodiment rather than alimitation. As a hypothetical example a lead line labeled

14 in FIG. 1A would indicate the longitudinal direction of framework 14.If an identification number corresponds to a grouping of parts, then anX, Y, Z, x, y, z,

,

, or

, followed by the identification number indicates the direction for allparts in the grouping of parts. As a hypothetical example, an arrowlabeled Y 412 in FIG. 9 would indicate the direction of greateststrength for the material constituting all of the web-members ininternetworking web array 412. Any set of linear directions can begeneralized to any curvilinear coordinate system such as a paraboloidalcoordinate system, ellipsoidal coordinate system, spherical coordinatesystem, cylindrical coordinate system.

FIG. 1A illustrates a structure 10 with four structural members or 1D(uniaxial) frameworks, including vertical structural members or verticalframeworks 12, 14 and horizontal structural members or horizontalframeworks 16, 18. In embodiments of structure 10, vertical frameworks12, 14 function as studs, jack studs, cripple studs, posts, or mullionswhile horizontal frameworks 16, 18 function as top plates, double topplates, bottom plates, transoms, headers, sole plates, or sill plates.Vertical frameworks 12, 14 are mounted on horizontal frameworks 16, 18.Horizontal framework 18 is mounted to the upper ends 20, 22 of thevertical frameworks 12, 14, respectively. Horizontal framework 16 ismounted to the lower ends 24, 26 of the vertical frameworks 12, 14,respectively. Each framework comprises first frame member or first chord31, second frame member or second chord 33 and central frame member orthird (struts) chord 35, which in the embodiment of FIG. 1A aregenerally parallel to one another. For structural insulation purposesthe first, second, and third chord 31, 33, 35, of each horizontalframework 16 are preferably mounted to the first, second, and thirdchord 31, 33, 35 of the vertical frameworks 12, 14, respectively, asshown in FIG. 1A. Each middle chord has a connecting member or webmember on each side. Each connecting member or web member connects anelongated frame member or chord to an adjacent chord. For instance,framework 18 has at least a first connecting member or web-member 32between chords 31, 33 in the normal

32 direction which in the embodiment shown is positioned at the terminalend 37 of horizontal framework 18 in the longitudinal

32 direction. Framework 18 has at least a second web-member 34 betweenchords 33, 35 in the normal direction which in the embodiment shown ispositioned at the terminal end 39. The embodiment shown in FIG. 1A alsohas a third web member 32 b between chords 31, 33 in the lateraldirection which is positioned longitudinally away from first web member32, proximal to terminal end 39. The spacing between web members 32, 32b is chosen to match the spacing between vertical frameworks 12 and 14or vice versa in a preferred embodiment like the one shown. In theembodiment shown in FIG. 1A there is also a fourth web-member 34 bpositioned longitudinally away from first web member 34, proximal toterminal end 37. In the embodiment shown in FIG. 1A, the fourthweb-member 42 b is longitudinally positioned half way betweenweb-members 32, 32 b. This preferred relative positioning of web-members32, 32 b, 34 produces a preferred metric path 42 through web member 32 band 34 b in framework 18. The intra-framework spacing of web-members invertical frameworks might not or might (shown) match that of horizontalframeworks. Another embodiment (not shown) with web-member 34 bpositioned a third of the way between web-members 32, 32 b would producea greater path length and therefore greater resistance for metric path42 but a lesser path length and therefore lesser resistance for the mostdirect metric path through web members 32 and 34 b. The preferredembodiment shown in FIG. 1A has the same relative spacing between anygiven pair of web members. Therefore, the most direct metric paththrough any given pair of web members has the same spanwise indirectnessas the preferred metric path 42. In a preferred embodiment with deeperframing members, the intra-framework spacing of web-members in thelongitudinal direction of the framing members would be greater topreserve the level of spanwise indirectness. Web-members 32, 32 b form afirst web. Web-members 34, 34 b form a second web. In a preferredembodiment of a framework with three structural members, two webs, andconsistently spaced web members like the one shown in FIG. 1A, theweb-members in adjacent webs are longitudinally offset by half theintra-web spacing of web-members as shown.

Vertical frameworks 12, 14 and horizontal framework 16 haveconfigurations similar to that of horizontal framework 18. Verticalframework 14 is attached at the terminal ends of horizontal frameworks16, 18 whereas vertical framework 12 is proximal to but not attached atthe terminal ends of horizontal frameworks 16, 18 to permit attachmentto other frameworks and to provide an unobstructed view of the terminalends of horizontal framework 16 in the figure. In other embodiments,vertical framework 12 would be attached at the terminal ends ofhorizontal frameworks 16,18 to form a rectangular structure. In suchembodiments vertical framework 12 would be preferably rolled 180° aroundits longitudinal

axis such that web-member 34 b would lie closest to the web-member atthe left end of horizontal framework 16.

Another embodiment (not shown) of the structure in FIG. 1A, incorporatesa different embodiment of vertical framework 12 having a longitudinalspacing between web-members 34, 34 b that differs from the on-centerspacing of web-members 34, 34 b in horizontal framework 18. Yet anotherembodiment (not shown) of the structure in FIG. 1A, incorporates adifferent embodiment of horizontal framework 18 in which thelongitudinal spacing of web-members 34, 34 b differs from the horizontalspacing of vertical frameworks 12, 14. An embodiment for which thelongitudinal spacing of web-members 34, 34 b equals the horizontalspacing of vertical frameworks 12, 14 produces larger values of spanwiseindirectness for metric paths in the transverse direction z. Yet anotherembodiment (not shown) of the structure in FIG. 1A, incorporates anotherembodiment of horizontal framework 18 in which web-members 32, 32 b havea greater length and extend down between structural members 31, 33 ofother embodiments of vertical frameworks 12, 14 for which theweb-members nearest ends 20, 22 are positioned further down toaccommodate. Yet another embodiment (not shown) of the structure in FIG.1A, incorporates another embodiment of vertical framework 12 in whichthe web-members nearest end 20 has a greater length and extends upbetween chords 31, 33 of horizontal framework 18. In this embodimentframework 18 is horizontally shifted enough to accommodate. One can alsodefine the normal direction for an energy barrier with an interiorsurface and exterior surface comprising any number frameworks. Thenormal direction runs along the line of closest approach between theinterior and exterior surfaces of the barrier at any given point oneither surface. Frameworks are preferably oriented so that the normaldirection of the framework substantially parallels the normal directionof the barrier.

FIG. 1B illustrates the framework 10′ containing a hardenable insulativematerial or solid insulation. The framework 10′ includes a central (gap)cavity 44′ containing an insulating segment 46′ formed from aninsulating material. Additionally, FIG. 1B illustrates a firstrectangular cavity 49′ defined by opposite-facing surfaces, i.e. innerfacing surface 50′ of chord 31′ and opposing surface 52′ of chord 33′,and opposite surfaces 54′, 56′ of web-members 32′, 32 b′, respectively.Rectangular cavity 49′ contains an insulating segment 58′ formed from aninsulating substance. The insulating substance used for insultingsegment 58′ may be the same or different insulating substance as is usedfor insulating segment 46′. Another type of rectangular cavity, i.e.rectangular cavity 62′ is defined by three surfaces, i.e. inner facingsurface 51′ of chord 31′, opposite surface 53′ of chord 33′, and outerside surface 64′ of web member 32′. The length of cavity 62′ extends tothe edge 66′ of the framework 10′. Rectangular cavity 62′ contains aninsulating segment 63′. The insulating substance used for insultingsegment 63′ may be the same or different insulating substance as is usedfor insulating segment 46′ or insulating segment 58′. All other cavitiesbetween parallel chords are similarly created as 49′ and 62′ andoptionally may contain similar insulating segments formed from a singletype, or different types of insulating substances. Each embodiment of aninsulatable insulative framework apparatus has a first relatedembodiment that comprises factory-installed insulation within thecavities and a second related embodiment that comprisesinstaller-installed insulation within the cavities. For example one suchembodiment comprises the vertical members 12 and 14 shown in FIG. 1B andrigid foam or other rigid insulation that holds the vertical frameworks12 and 14 in the configuration shown in FIG. 1B as a prefabricated panel10′ so that an installer can efficiently make structural connections,that more permanently hold the configuration shown in FIG. 1B, byfastening the horizontal frameworks 16 and 18 to the vertical frameworks12 and 14 and other vertical frameworks perhaps in a similar type ofpanel. In a more specific version of this embodiment, the verticalframeworks 12 and 14 are made from a wood product and function as studs.The horizontal frameworks 16 and 18, once attached to the prefabricatedpanel, function as the bottom and top plate of an insulated wall. Inanother such embodiment the longitudinal

14 axis of the prefabricated panel is oriented in the horizontal xdirection to function as a floor panel. In another such embodiment thelongitudinal

14 axis of the prefabricated panel is oriented horizontally or pitcheddiagonally to function as a roof panel. An embodiment of the horizontalframework 16 has factory-installed solid insulation fixed between anynumber of the cavities so as to eliminate the labor required to installinsulation on site. An embodiment of the vertical framework 12 hasfactory-installed solid insulation fixed between any number of thecavities so as to eliminate the labor required to install insulation onsite.

In other embodiments, the framework 10 can be positioned along anyintrinsic direction to any suitable position and rotated around anyintrinsic angle to any suitable orientation. The frameworks may rundiagonally with respect to the horizontal, vertical, or transversedirections. In the embodiments shown in FIGS. 1A and 1B, the web membersare shown as extending in a direction generally perpendicular to thechords, however, in different embodiments, for example that shown inFIG. 2AA, at least one web member is pitched diagonally relative to thechords. In other embodiments, not shown, at least one web member extends(b) diagonally yawed relative to the chords.

FIG. 1C shows representative metric path set 1CX for framework 1C. Eachblack dot represents a start point for a different metric path astypified by start points 1CA3A, 1CB2A, 1CC1A, 1CD4A, 1CD3A. Eachbullseye dot represents an end point of a metric path as typified by endpoints 1CA3F, 1CB2F, and 1CC1F. The representative metric paths convergeto a focal point as typified by focal point 1CDXF which overlaps the endpoints for the metric paths with start points 1CD4A and 1CD3A and allother metric paths that converge to focal point 1CDXF. Any end pointthat overlaps a focal point can serve as a representative of the focalpoint. Thus, end points 1CA3F, 1CD2F, 1CC1F, and 1CDXF represent focalpoints one, two, three, and four, respectively. Each focal point definesa bundle of metric paths that all converge on the same focal point orpass through the same focal point. Thus, focal points one, two, three,and four define bundles A, B, C, and D, respectively. For instance, allmetric paths that pass through or converge to focal point 1CDXF formbundle D. Each bundle of metric paths includes a set of special paths,i.e. the most-direct metric through-path which passes through thedefining focal point in addition to the shortest metric path,most-direct metric path, longest minor metric path, and longest metricpath which converge on the defining focal point.

FIG. 1D shows examples of the special metric paths within differentbundles. For instance, the longest metric path in bundle D is the paththat originates at start point 1CD4A and terminates at focal point 1CDXFas shown in FIG. 1D. The longest minor metric path in bundle C is thepath that originates at start point 1CC3A and terminates at focal point1CC3F as shown in FIG. 1D. The most direct metric path in bundle B isthe path that originates at start point 1CB2A and terminates at focalpoint 1CB2F as shown in FIG. 1D. The shortest metric path in bundle A isthe path that originates at start point 1CA1A and terminates at focalpoint 1CA1F as shown in FIG. 1D. The most direct metric through-path inbundle B shown in FIG. 1E is the path that originates at point 1CB5A,runs through point 1CB2F (shown in FIG. 1C) and terminates at point1CB5G. The most direct metric through-path and most direct metric pathrequire further explanation. If framework 1C has well-defined outermostnormally facing surfaces, then the most direct metric path in bundle Bmay be defined as the shortest metric path in bundle B that originateson an outermost normally facing surface. If framework 1C does not havewell-defined outermost normally facing surfaces, then a more generaldefinition is needed. More generally the most direct metric path inbundle B is defined as a metric path in bundle B with a length L, spanS, and directness L/S greater than that of any other metric path inbundle B. To show that the path originating at start point 1CB2A inbundle B and terminating on point 1CB2F is the most direct metric pathin bundle B one must prove that no other metric path in bundle B has agreater value of directness. To do so, start by proving that the mostdirect metric path in bundle B has a greater value of directness thanthat of the shortest metric path in bundle B (shown in FIG. 1F). Thepath segment of the most direct metric through-path beyond point 1CB1Ais identical to the shortest metric path having the same length L, samespan S, and same directness D equal to L/S. Up to the point 1CB1A anymetric path that deviates from the shortest metric path in a directionparallel to a span-wise direction line by a positive amount ΔS will havea span equal to S+ΔS and a length equal L+ΔS such that the directness Dequals (S+ΔS)/(L+ΔS). A directness D of (S+ΔS)/(L+ΔS) is greater thanS/L in proportion to the magnitude of ΔS. The most-direct metric path inbundle B shown in FIG. 1D has the greatest possible deviation ΔS in thespanwise direction and thus has the largest value of directness. Up tothe point 1CB1A any metric path that deviates from the shortest metricpath in a direction parallel to a span-wise direction line by a positiveamount ΔS and deviates in a direction perpendicular to a span-wisedirection line by a positive amount Δ

will have a span equal to S+ΔS and a length equal L+(ΔS²+Δ

²)^(1/2) such that the directness D equals (S+ΔS)/{L+(ΔS′+Δ

²)^(1/2)}. A directness D equal to (S+ΔS)/{L+(ΔS2+Δ

²)^(1/2)} is always less than (S+ΔS)/(L+ΔS) for all positive values ofΔS and positive values of Δ

. The same argument applies to any other possible combination ofmultiple deviations from the most direct metric path. Any number ofdeviations always leads to a metric path with a lesser value ofdirectness than the most direct metric path.

Similarly, the most direct metric through-path also requires furtherexplanation. If framework 1C has well-defined outermost normally facingsurfaces, then the most direct metric through-path in bundle B may bedefined as the shortest bound path in bundle B that runs between theoutermost normally facing surfaces. If framework 1C does not havewell-defined outermost normally facing surfaces, then a more generaldefinition is needed. More generally the most direct metric through-pathin bundle B is defined as the most direct bound path in bundle B, i.e.,a bound path in bundle B with a length L, span S, and directness L/Sgreater than that of any other bound path in bundle B. To show that thepath originating at start point 1CB5A in bundle B and terminating onpoint 1CB5G is the most direct bound path in bundle B one must provethat no other bound path in bundle B has a greater value of directness.To do so, start by proving that the most direct metric through path inbundle B has a greater value of directness than that of the most directmetric path in bundle B (shown in FIG. 1F). The most direct metric pathand most direct metric through-path are identical up to point 1CB1Fhaving the same length L, same span S, and same directness D equal toL/S. Beyond point 1CB1F any bound path that deviates from the mostdirect metric path in a direction parallel to a span-wise direction lineby a positive amount ΔS will have a span equal to S+ΔS and a lengthequal L+ΔS such that the directness D equals (S+ΔS)/(L+ΔS). A directnessD of (S+ΔS)/(L+ΔS) is greater than S/L in proportion to the magnitude ofΔS. The most-direct metric through-path shown in FIG. 1D has thegreatest possible deviation ΔS in the spanwise direction and thus hasthe largest value of directness. Beyond point 1CB1A any bound path thatdeviates from the most direct metric path in a direction parallel to aspan-wise direction line by a positive amount ΔS and deviates in adirection perpendicular to a span-wise direction line by a positiveamount Δ

will have a span equal to S+ΔS and a length equal L+(ΔS²+Δ

²)^(1/2) such that the directness D equals (S+ΔS)/{L+(ΔS²+Δ

²)^(1/2)}. A directness D equal to (S+ΔS)/{L+(ΔS²+Δ

²)^(1/2)} is always less than (S+ΔS)/(L+ΔS) for all positive values ofΔS and positive values of Δ

. The same argument applies to any other possible combination ofmultiple deviations from the most direct metric path. Any number ofdeviations always leads to a metric path with a lesser value ofdirectness than the most direct metric path. To be completely accurateone must describe the path in FIG. 1D as the most direct metricthrough-path in a normal direction in bundle B. The most direct metricthrough-path has the extremely powerful geometrical feature of runningbetween the outermost surfaces of a framework in the span-wise directionof the most direct metric through-path no matter how the outermostsurfaces are shaped.

The longest metric path in any given bundle is a metric path with alength such that the length is greater than that of any other metricpath in the bundle. The shortest metric path in any given bundle is ametric path with a length such that the length is less than that of anyother metric path in the bundle. The longest minor metric path in anygiven bundle is a metric path with a length such that the length isgreater than that of any other metric path in the bundle starting at anypoint on the opposite side of the most direct metric path relative tothe start point of the longest metric path. The set of locallymost-direct metric paths in any specified direction is a set includingeach most direct metric path in the specified direction from eachbundle. The set of locally shortest metric paths in a specifieddirection is a set including each shortest metric path in the specifieddirection from each bundle. The set of locally most-direct metricthrough-paths in a specified direction is a set including each mostdirect metric through-path in the specified direction from each bundle.The set of locally longest metric paths in a specified direction is aset including each longest metric path in the specified direction fromeach bundle. The set of locally longest minor metric paths in aspecified direction is a set including each longest minor metric path inthe specified direction from each bundle. Each of these sets defines aset of values for each physical property of interest such as pathlength. Each set of values for each physical property of interest thendefines a set of statistical values for each statistical function ofinterest such as a statistical average. In that way the statisticalaverage path length for the set of locally most-direct metricthrough-paths is available to characterize an insulatable, insulativeframework apparatus. A non-limiting list of physical properties ofinterest include path length, span, range span-wise indirectness,range-wise indirectness, structurally insulative resistance,structurally insulative resistivity, structural insulation factor, andother physical properties. A non-limiting list of statistical functionsof interest includes maximum, minimum, standard deviation, average,uniformity, count, and other statistical functions. For example, theaverage spanwise indirectness for the locally most-direct metric pathsin the normal direction of uniaxial framework 1C means the statisticalaverage for the set of each spanwise indirectness value for eachmost-direct metric path in each bundle of the framework. If no type ofmetric path is specified for a statistical function then the statisticalfunction applies to all metric paths excluding the through-paths. Forinstance, the average spanwise indirectness means the average of the setof spanwise indirectness values for the representative set of metricpaths.

If no bundle is specified then (1) the term shortest metric path means ametric path with a length such that the length is less than that of anymetric path in any bundle, (2) the term longest metric path means ametric path with a length such that the length is greater than that ofany metric path in any bundle, (3) the term longest minor metric pathmeans a metric path with a length such that the length is less than thatof any minor metric path in any bundle, (4) the term most-direct metricpath means a metric path with a directness such that the directness isgreater than that of any metric path in any bundle, (5) the termmost-direct metric through-path means a bound path with a directnesssuch that the directness is less than that of any bound path in anybundle. For example, FIG. 1G shows the shortest metric path in thenormal direction for framework 1C. As another example, FIG. 1H shows themost-direct metric through-path for framework 1C.

FIG. 2AA shows a framework with three structural members and diagonallypitched web members. The pitch angles shown are substantially less than±45° relative to the chords, i.e. 15°. The diagonal web members in FIG.2AA could have alternating pitch angles of ±45° relative to the chords.The diagonal web members in different layers create a chevron pattern.Another embodiment (not shown) has web members with a diagonal pitch anda diagonal yaw relative to the structural members.

FIG. 2AB shows three parallel chords with a single row of diagonalbraces positioned between each set of adjacent chords. This frameworkhas diagonal braces/web-members with a constant intra-layer brace/webspacing and the maximum characteristic offset betweenbraces/web-members, with the same pitch-angle sign, in different layers.

FIG. 2AC shows framework 1900 with a single open web of straightdiagonal web members interconnecting two parallel chords. The webmembers for this type of embodiment have a characteristic pitch angleØy₁₉₀₀ relative to the bottom chord of less than 40°. The characteristicpitch angle Øy₁₉₀₀ for the embodiment shown in FIG. 2AC is 15° withalternating positive and negative signs. U.S. Pat. No. 3,452,502, thecontents of which is hereby incorporated by reference in its entirety,discloses a method of joining two diagonal web-members with each otherand a chord of a truss using finger joints. Embodiments of diagonal-webtrusses described herein include this type of finger joint as well asany other type of woodworking joint.

FIG. 2AD shows truss 1900′, the same as truss 1900, except with a singlestraight diagonal web member 1902 interconnecting two chords 1901, 1903at a separation distance Δz₁₉₀₁₃. Straight diagonal web member 1902 hasa pitch angle Øy₁₉₀₁₂ relative to chord 1901 of 15°. Straight diagonalweb member 1902 has a thickness Δ

₁₉₀₂ equal to half the separation distance Δz₁₉₀₁₃. The pitch angleØy₁₉₀₁₂, thickness Δ

₁₉₀₂, and separation distance Δz₁₉₀₁₃ determine the shortest paththrough the structure from chord 1901 to chord 1903 which is shortestmetric path 1904. Shortest metric path 1904 has a 29° pitch angleØy₁₉₀₁₄ relative to chord 1901, a span S₁₉₀₄ equal to the separationdistance Δz₁₉₀₁₃, and a length L₁₉₀₄ equal to 2 times the separationdistance Δz₁₉₀₁₃. The structural insulation factor F₁₉₀₄ for shortestmetric path 1904 equals L₁₉₀₄ divided by S₁₉₀₄, that is 2. If straightdiagonal web member 1902 is made from a material with an isotropicresistivity r₁₉₀₂ then the structurally insulative resistivity r_(s1902)equals the resistivity r₁₉₀₂ multiplied by the structural insulationfactor which in this case is 2·r₁₉₀₂. The physical quantity of span-wiseindirectness, I, specifies the improvement in resistivity afforded bythe structural insulation factor, i.e., {2·r₁₉₀₂−r₁₉₀₂}/r₁₉₀₂ which alsoyields the definition {r·(L/S)−r}/r which simplifies to I={L/S−1}.Herein the span-wise indirectness is expressed as a percentage byconvention. For the embodiment shown in FIG. 2AD the span-wiseindirectness equals {2·r₁₉₀₂−r₁₉₀₂}/r₁₉₀₂. Thus, truss 1900′ has aspan-wise indirectness of 100% which corresponds to a 100% improvementin structurally insulative resistivity for an isotropically resistivematerial. For any span-wise indirectness I and isotropic resistivity r,the structurally insulative resistivity is {I+1}·r. In an embodimentpreferred for strength, the strong axis of the material that constitutesweb member Y ₁₉₀₂ is oriented parallel to the longitudinal

₁₉₀₂ direction of web member 1902. In another embodiment preferred forresistance, the strong axis of the material that constitutes web memberY ₁₉₀₂ is oriented perpendicularly or substantially non-parallel to thelongitudinal

₁₉₀₂ direction of web member 1902. These variations in orientation ofthe strong axis of a material relative to the axis of the structuralpart it constitutes apply to all embodiments.

For comparison with framework 1900, FIG. 2AE shows a control in the formof truss 2000 with two chords 2001, 2003 at a separation distanceΔz₂₀₀₁₃ interconnected by a straight diagonal web member. Straightdiagonal web member 2002 has a pitch angle Øy₂₀₀₁₂ relative to chord2001 of 45°. Straight diagonal web member 2002 has a thickness Δ

₂₀₀₂ equal to half the separation distance Δz₂₀₀₁₃. The pitch angleØy₂₀₀₁₂, thickness Δ

₂₀₀₂, and separation distance Δz₂₀₀₁₃ determine the shortest paththrough the structure from chord 2001 to chord 2003 which is shortestmetric path 2004. Shortest metric path 2004 has a pitch angle Øy₂₀₀₁₄relative to chord 2001 of 75°, a span S₂₀₀₄ equal to the separationdistance Δz₂₀₀₁₃, and a length L₂₀₀₄ equal to 1.04 times the separationdistance Δz₂₀₀₁₃. The structural insulation factor F₂₀₀₄ for shortestmetric path 2004 equals L₂₀₀₄ divided by S₂₀₀₄, that is 1.04. If truss2000 is made from a material with an isotropic resistivity r then thestructurally insulative resistivity equals the resistivity r multipliedby the structural insulation factor which in this case is 1.04r.

For comparison, truss 2005 shown in FIG. 2AF incorporates chords 2006and 2008 with a separation distance Δz₂₀₀₆₈ interconnected by a straightdirect web member 2007 with a pitch angle Øy₂₀₀₆₇ relative to chord 2006of 90°. These quantities determine that the shortest metric path 2009between chords 2006 and 2008 has a length L₂₀₀₉ and span S₂₀₀₉ equal tothe separation distance Δz₂₀₀₆₈ and a structural insulation factor USequal to 1. If truss 2005 is made of the same material as truss 2000with isotropic resistivity r, then the structurally insulativeresistivity equals the resistivity r multiplied by the structuralinsulation factor which equals r. Thus, truss 2000 offers an improvementof {1.04·r−r}/r, that is 4%, over truss 2005. Span-wise indirectnessquantifies this improvement as {length/span}−1. For instance, shortestmetric path 2004 has a span-wise indirectness I₂₀₀₄ equal to{L₂₀₀₄/S₂₀₀₄}−1, that is 4%, so the geometry of truss 2004 offers animprovement of 4% to the structurally insulative resistivity.

The straight-diagonal-web-member two-chord trusses in FIG. 2AC and FIG.2AD compensate for the effects described for truss 2005 by (1) makingthe most direct metric path length between the chords a greaterpercentage of the inter-chord length of the diagonal web member, (2)lessening the linear density of material along the longitudinaldirection of the chords, (3) still allowing for an increase in lateralextent of material in comprising the truss, (4) increasing the leastangle between the shortest metric path and the local span-wisedirection, (5) providing a greater area for the web member to interfacewith the chords which strengthens the joint, and (6) increasing thelength L of the most direct metric path relative to its span S therebyincreasing the structural insulation factor L/S and (a) increasing theresistance R=r·L along the most direct metric path where r is theresistivity approximately parallel to

₂₀₀₂ or equivalently (b) increasing the structurally insulativeresistivity of the web member, r_(s)=r_(val)·L/S. Table 1A summarizesuseful formulae and Table 1B summarizes the symbols and terminology. Me,associated with an angle relative to the span of a metric path, in thetable corresponds to the span-wise slope of a tangent line (change innormal direction divided by change in longitudinal direction or changein lateral direction divided by change in longitudinal direction) to anystraight subpath of the most direct metric path or shortest metric path.Me, associated with an angle relative to the chords, in the tablecorresponds to the slope of a tangent line (change in longitudinaldirection divided by change in normal direction or change inlongitudinal direction divided by change in lateral direction) to anystraight subpath of the most direct metric path or shortest metric path.

TABLE 1A R_(sval) = r_(val) · L, (1) R_(val) = r_(val) · S (2) F =R_(sval)/R_(val) = L/S (3) I = R_(sval)/R_(val) − 1 = L/S − 1 = (L −S)/S (4) M⊖ = [(L² − S²)^(1/2)]/S (5) M⊖ = [(L/S)² − 1]^(1/2), = [ F² −1]^(1/2) = (6) (I² + 2 · I)^(1/2) F = L/S = I + 1 = (M² + 1)^(1/2), (7)I = (M² + 1)^(1/2) − 1, (8) ΔR_(sval) = R_(sval) − R_(val) = r_(val) ·(L − S) = (9) r_(val) · I · S = r_(val) · (F − 1) · S r_(sval) =R_(sval)/S = r_(val) · L/S = r_(val) · F = r_(val) · (I + 1) (10) Δr_(sval) = ΔR_(val)/S = r_(val) · (L − S)/S = r_(val) · (F − 1) =r_(val) · I (11)  F = L/S = R_(sval)/R_(val) = r_(sval)/r_(val)·, (12) r_(dir) = r_(target) or R_(dir) = R_(target) (13)  r_(sval) = r_(target)or R_(sval) = R_(target) (14)  M⊖ = [(r_(sval)/r_(val))² − 1]^(1/2) =(15)  [(r_(target)/r_(val))² − 1]^(1/2) M⊖ ≈ r_(target)/r_(val), forr_(target)/r_(val) >> 1. (16)  Mø = 1/M⊖ (17) 

TABLE 1B S span of the metric path L length along the metric pathR_(val) areal resistance R_(Sl) areal resistance (metric units) R_(sval)structurally insulative resistance R_(Sls) structurally insulativeresistance (metric units) r_(sval) structurally insulative resistivityr_(val) direct resistivity F structural insulation factor I span-wiseindirectness M⊖ metric path slope relative to the span-wise direction Mømetric path slope relative to a structural member

FIG. 2AH shows uniaxial framework 1000 which possesses three chords1001, 1003, 1005 and two webs 1002, 1004 like uniaxial framework 12 inFIG. 1A. Webs 1002, 1004 each comprise at least one web member 1002 a,1004 a, respectively. Webs 1002, 1004 comprise terminal web members1002N and 1004N which could be the same as web members 1002 a, 1004 a ina framework with only one web member in each of webs 1002 a, 1004 a. Forthe embodiment shown in FIG. 1A, web 1002 incorporates web members 1002a, 1002 b, 1002N and web 1004 incorporates web members 1004 a, 1004N.For the embodiment shown in FIG. 1A, web 1002 incorporates floatingtenons 1002 a′, 1002 b′, 1002N′ and web 1004 incorporates floatingtenons 1004 a′, 1004N′. The two wavy lines 1009 indicate the possibilityfor additional length of chords 1001, 1003, 1005, additional webmembers, and additional floating tenons. Table 2 shows preferred valuesfor the key dimensional parameters. Preferred dimensional parameters forany other embodiment can be obtained by multiplying these parameters bya scaling factor. For instance, multiplication by a scaling factor of 2produces the preferred dimensional parameters of an 11 inch (˜280 mm)deep framework.

TABLE 2 Imperial Units SI Units Dim. Preferred Preferred Param. ValueRange Value Range Δ 

 ₁₀₀₀ 5.5 in 5-7 in 148 mm 123-175 mm Δ 

 ₁₀₀₂  24 or 16 in 12-36 in 600 mm 300-900 mm Δ 

 _(10024′) 12 or 8 in 6-24 in 300 mm 150-450 mm Δ 

 _(1004a)  2.4 or 1.5 in 0.75-3 in 61 or 48 mm 19-75 mm Δ 

 ₁₀₀₁  ¾ or 1.1 in 0.5-2.5 in 19 or 30 mm 12-61 mm Δ 

 ₁₀₀₂ 1¼ or 1.1 in 0.5-2.5 in 36 or 30 mm 12-61 mm Δ 

 ₁₀₀₃ 1⅛ or 1.1 in 0.5-2.5 in 36 or 30 mm 12-61 mm Δ 

 ₁₀₀₄ 1.25 or 1.1 in 0.5-2.5 in 36 or 30 mm 12-61 mm Δ 

 ₁₀₀₅ 1.125 or 1.1 in  0.5-2.5 in 36 or 30 mm 12-61 mm Δ 

 ₁₀₀₅₀ 3.0625 or 0 in    0-6 in  0 mm 0-150 mm Δ 

 _(1005′) 92.625 or 96 in or 72-288 in 2400 mm  1800-7200 mm 104.625 or108 in

FIG. 2B is a control schematically showing a chord 230 with no webmembers and can be described by code 1. FIGS. 2C-2I schematically showvarious embodiments of 1D (uniaxial) frameworks with each pair of chordsconnected by a web of diagonally pitched web members.

FIG. 2C shows a chord having a vertical row of pitched diagonallyextending web members 236 connected thereto, and can be described bycode 1a.

FIG. 2D shows an embodiment similar to that of FIG. 2C except that thedirection of the diagonal braces is reversed. This embodiment isdescribed by code 1b.

FIG. 2E show three parallel chords with a single row of diagonal bracespositioned between each set of adjacent chords. In FIG. 2E, horizontallyspaced diagonal braces extend in different directions from one another.This embodiment shows constant intra-layer web-member spacing and acharacteristic offset of zero between braces/web-members, with the samepitch-angle sign, in different webs and can be described by code 1a1a1.Horizontally spaced diagonal braces are substantially parallel to oneanother.

FIG. 2F shows 2 chords and two sets of diagonal braces, one set to theright of each chord. This framework is a code 1a1a framework which isthe same as FIG. 2E except with one peripheral chord omitted.

FIG. 2G is similar to FIG. 2E except that the braces spaced in thevertical direction from one another have a different alternatingpattern. This is a code 1a1a1 framework with diagonal web memberssloping one way in the first half of the framework and then the oppositeway along the second half of the framework along longitudinal axis.

FIG. 2H is similar to FIG. 2E except all of the diagonal braces areparallel to one another. This code 1a1a1 framework has diagonal webmembers sloping one and only one way. For any framework of this type onecan omit one or both of the peripheral struts/chords. For someembodiments of the framework in FIGS. 2C-2I some or all adjacent webmembers in the same horizontal layer touch one another like theembodiments shown in FIGS. 2A and 2B. For other embodiments of theframework in FIGS. 2C-2I (not shown), some or all adjacent web membersin the same horizontal layer do not touch one another as in theembodiments shown in FIGS. 3C, 3F. Some embodiments incorporatehalf-unit-cells and an odd number of web members per horizontal layer ofweb members. The number of web members per horizontal layer of webmembers ranges between one and any positive integer.

FIG. 2I shows four chords with diagonal braces therebetween.Horizontally spaced braces are parallel to one another. Verticallyspaced braces alternate in their diagonal direction. This can bedescribed as a code 1a1a1a1 framework with two units cells, 4struts/chords, and 3 layers of diagonal braces/web-members with aconstant intra-layer brace/web spacing and an interlayer characteristicoffset of zero between same-polarity web members.

FIG. 2J shows four chords with diagonal braces therebetween.Horizontally spaced braces alternate in their diagonal direction.Vertically spaced braces also alternate in their diagonal direction.This can be described as a code 1a1b1a1 framework with two units cells,4 struts/chords, and 3 layers of diagonal braces/web-members with aconstant intra-layer brace/web spacing and a maximum interlayercharacteristic offset between same-polarity braces/web-members. FIG. 2Kshows five chord with diagonal braces therebetween. This is a code1a1b1a1b1 framework with two units cells, 5 struts/chords, and 4 layersof diagonal braces/web-members with a constant intra-layer brace/webspacing and a maximum interlayer characteristic offset betweensame-polarity braces/web-members.

FIGS. 2M-2T schematically show various embodiments of uniaxial/1Dframeworks with straight braces. The framework in each figures shows 1.5unit-cells with each pair of chords connected by a web containing twoweb-members.

FIG. 2M shows 1 chord 330 with two straight web members 336 attachedthereto. This framework is a control described with code 1a.

FIG. 2N shows 1 chord with two straight web members attached at lowervertical locations than the embodiment of FIG. 2B, but withsubstantially the same spacing from one another as in the embodiment ofFIG. 2B. This framework is a control described with code 1a.

FIG. 2O shows three chords with two straight web members between eachset of adjacent chords. The pair of web members between the first andsecond chords is vertically higher than the pair of web members betweenthe second and third chords. This framework has a code of 1a1b1.

FIG. 2P depicts four chords with two straight web members between eachset of adjacent chords. The pair of web members between the first andsecond chords is at the same vertical height as the pair of web membersbetween and third and fourth chords, following a pattern of code1a1b1a1.

FIG. 2Q shows four chords with two straight web members between each setof adjacent chords. Each pair of web members is at a different verticalheight than the other pairs of web members, following a pattern of code1a1b1c1.

FIG. 2R depicts five chords and four pairs of straight members. Thevertical height of the first and third pairs of web members is the same.The vertical height of the second and fourth pairs of web members is thesame. This arrangement follows the pattern of code 1a1b1a1b1.

FIG. 2S shows three chords in a pattern of code a1b1a1b with no chord onthe left, showing that a web can be left unconnected on one side so asto create an extra layer of insulatable cavities when connected toanother object.

FIG. 2T shows four chords in a pattern of code 1a1b1o in which oindicates a web of horizontally extending web members running intoand/or out of the page. In this case, the web members do not connect twochords in the normal direction but function to connect a chord in oneframework (shown) to a laterally disposed chord in one or more than oneother framework (not shown).

For the most direct metric path in the normal and/or lateral directionof a framework that defines a span, a path length, a range, a rangewiseindirectness, a spanwise indirectness, and a greatest web memberthickness parallel to the span, (1) the ratio of the path length to themaximum web member thickness is less than a certain amount, (2) themaximum web thickness is greater than a certain percentage of the span,and (3) the framework has at least one of (A) a rangewise indirectnessgreater than 0% and spanwise indirectness greater than x or rangewiseindirectness equal to zero and spanwise indirectness greater than y in apreferred embodiment of the framework for any application.

FIGS. 3A-3F show six non-limiting examples of web shapes in ahalf-unit-cell of framework 129. Each web shape is shown between twoadjacent chords. The vertical lines in each of FIGS. 3A-3F schematicallyshow chords as shown by labeled chords 130 and 132 in FIG. 3A. Thedotted lines 104, 106, 108, 110 and 112 between adjacent chordsschematically show webs 104, 106, 108, 110, and 112 between chords 130and 132. Web 104 shown in FIG. 3A is straight and runs diagonallybetween the chords 130 and 132. A preferred embodiment of a frameworkapparatus to have no thermal bridging upon installation in an insulated,wood-frame building with a resistivity of approximately r1 for the wallcavity insulation, comprises the FIG. 3A truss made from a material witha resistivity of approximately r2 along the longitudinal direction ofthe diagonal web member 140, wherein the diagonal web member 104 has aslope (Δy/Δx) substantially equal to r1 divided by r2, the x and ydirections are shown in the FIG. 3A, and the resistivities have thermalunits of ° F.·sqft per BTUh per inch as a non-limiting example.

The web shown in FIG. 3B incorporates a third chord 131 and two webs 105and 107 which function together as a web-like structural member 106. Web108 shown in FIG. 3C is similar to web-like structural member 106 inthat web members 105 and 107 are present in both web 108 and 106 and webmember 131′ connects web member 105 and 107 as does structural member131. However, web member 131′ is not a structural member like structuralmember 131. Thus, web 108 is not a web-like structural member becauseweb 108 does not include a structural member. Instead thestructural-member like segment 131′ does not run the entire longitudinallength of the half-unit-cell delimited by black circles in FIG. 3C. Eachembodiment with a half-unit-cell shape like that of web 106 has arelated embodiment with a shape like that of web 104, 108, 110, 112 andall other implicit web shapes. Each closed circle 102 in FIGS. 3A-3Frepresents an interface between a key pair of structural parts. Eachclosed circle 102 in FIGS. 3A-3F appears in a corresponding figure inthe grouping of FIGS. 4A-4F to illustrate the process of replicating ahalf-unit-cell to create a new framework. Generally, any half-unit-cellwith three structural members can be replaced by a half-unit-cell withtwo structural members and vice versa in embodiments where the shape ofthe web for the replacement half-unit-cell has an advantage. The samemethod applies to half-unit-cells with more than three structuralmembers. Generally, the spanwise indirectness can be preserved for suchreplacements although. Frameworks with a non-zero rangewise indirectnessgenerally provide a higher spanwise indirectness than frameworks withzero rangewise indirectness for any given span of the most direct metricpath along any targeted direction.

FIGS. 3G-3L show various web member shapes. FIGS. 4A-4F show sixnon-limiting examples of web shapes in the half-unit-cell of aframework. The web shapes are shown between adjacent chords in aframework that includes at least 3 chords.

For instance the FIG. 4A framework has three chords labeled 130′, 132′,and 132″. By comparison to the FIG. 3A framework, the FIG. 4A frameworkhas an additional chord, chord 132″.

The FIG. 4B framework has 5 chords labeled as 130′, 131′, 132′, 131″,and 132″. Chord 132″ is analogous to chord 132 in the sense that chord132″ is the last chord to the right in the figure and is the last chordin the structural-member-array comprising chords 130′, 131′, 132′, 131″,and 132″ just as chord 132 is the last chord to the right in FIG. 3A andis the last chord in the structural-member-array comprising chords 130,and 132. Chord 132″ has two labels 130″ and 132″. In the FIG. 4Bembodiment, chord 130″ is the same as chord 132″. In another embodiment(not shown) chord 130″ is attached to chord 132″ and they are differentobjects joined together. Each closed circle 102′ represents theinterface of a key pair of structural parts which is translated to theright and transformed into each open circle 100′ to illustrate theprocess of replicating a half-unit-cell to create a new framework. Thevertical lines schematically show chords as illustrated by chords 130′,132′ and 132″ in FIG. 4A. The dotted lines 104′, 106′, 108′, 110′ and112′ between adjacent chords 132′ and 132″ schematically show webmembers between chords 132′ and 132″.

FIGS. 5A-5F show six non-limiting examples of web shapes in thefull-unit-cell of a framework. Dashed lines 114′, 116′, 118′, 120′ and122′ represent a vertical reflection of the dashed lines 104′, 106′,108′, 110′ and 112′ in FIGS. 4A-4F. Dashed lines 104″, 106″, 108″, 110″and 112″ between adjacent chords 130′ and 132′ schematically show webmembers between chords 130′ and 132′ analogous to dashed lines 104, 106,108, 110 and 112 in FIG. 3A-3F. Dashed lines 114″, 116″, 118″, 120″ and122″ represent a vertical reflection of the dashed lines 114′, 116′,118′, 120′ and 122′. Each of FIGS. 5A-5F illustrates how to create a newframework by combining each framework of FIGS. 4A-4F, respectively, witha vertical reflection of each framework of FIGS. 4A-4F, respectively.

FIG. 6A shows a biaxial framework 610 comprises multiple pieces ofmaterial, i.e. structural parts, including a 3 by 3 matrix of chords, 2by 3 matrix of internetworking webs, and a 2 by 3 matrix ofintranetworking webs, wherein each internetworking web comprises aplurality of internetworking web members formed separately from thechords and each intranetworking web comprises a plurality ofintranetworking web members formed separately from the chords. Theinternetworking web members and intranetworking web members are arrangedso that biaxial framework 610 structurally insulates in any directionperpendicular to the chords. In other embodiments the interworking webmembers and/or intranetworking web members are formed as part of thestructural members. These structural parts can be conceptually groupedinto frameworks, intranetworking webs (webs within a framework) and intointernetworking webs (webs between frameworks) in more than one way astypified by the following example of a first conceptual grouping. Afirst layer 411 is framework 411. A second layer 412 is aninternetworking web array 412. A third layer 413 is framework 413 whichis a replica of framework 411. A fourth layer 414 is a internetworkingweb array 414 containing internetworking web-members that are offsetrelative to those of internetworking web array 412. A fifth layer 415 isframework 415 which is a replica of framework 411. Each of theinternetworking web arrays 412 and 414 comprise substantiallyperpendicular intranetworking web members. In other embodiments (notshown) the internetworking webs arrays 412 and 414 and the biaxialframework 610 comprise diagonal intranetworking web-members havediagonal intranetworking web-members in either pitch angle, yaw angle,or both the pitch and yaw angle. Each of the frameworks 411, 413 and 415comprise first and second intranetworking webs and first, second, andthird chords. Each of the frameworks 411, 413 and 415 has substantiallyperpendicular intranetworking webs. In other embodiments (not shown) theuniaxial frameworks 411, 413 415 and biaxial framework 610 have diagonalintranetworking web-members in either pitch angle, yaw angle, or bothpitch and yaw angles. In other embodiments (not shown) these frameworkshave diagonal web-members such that the biaxial framework 610 also hasdiagonal web members. Frameworks 411, 413 and 415 align in aside-by-side arrangement such that the first chords of the frameworkalign with each other, the second chords of the framework align witheach other, and the third chords of the framework align with each otherin a first non-limiting configuration.

Framework 411 is individually illustrated in FIG. 7. Internetworking webarray 412 is illustrated in FIG. 8 with framework 411 included toclarify the spatial web-to-framework relationship. Frameworks 413 and415 are replicas of the Framework 411 illustrated in FIG. 7.Internetworking web array 414 is illustrated in FIG. 10 with framework411 included to clarify the spatial web-to-framework relationship.Relative to a solid piece of the same material with the same dimensions,biaxial framework 410 reduces the flow of energy along its normal axisinto and out of the page along a diagonal line z sloping downwardly fromleft to right on the page, and also reduces the flow of energy along itslateral axis

, up and down the page in the direction shown by line y. This reductionin energy flow stems from the geometrical relationship between thestructural parts and the metric paths produced by that geometricalrelationship. The metric paths for biaxial framework 410 aresubstantially the same as the metric paths for biaxial framework 410,illustrated in FIG. 6D. A preferred embodiment of a framework apparatus,(not shown) for installation in an insulated building, comprises biaxialframework 410 and an insulating material that fills the cavities ofbiaxial framework 410.

A preferred embodiment of a framework apparatus, (not shown) forinstallation in an insulated, wood-frame building with 2×4 walls and anR-value of 13° F.·sqft per BTUh for the wall cavity insulation,comprises biaxial framework 410 made from a wood product to have anormal dimension of 3.5″, wherein the cavities of biaxial framework 410hold an insulating material with a thermal resistivity greater thanabout 2.6° F.·sqft per BTUh per inch to achieve minimum code compliancefor R5ci, that is an R-value of 5° F.·sqft per BTUh of continuousinsulation over the structural members.

A preferred embodiment of a framework apparatus, (not shown) forinstallation in an insulated, wood-frame building with 2×4 walls and anR-value of 13° F.·sqft per BTUh for the wall cavity insulation,comprises biaxial framework 410 made from a wood product to have anormal dimension of 3.5″ and a normal dimension totaling 1.5″ for thetwo cavities, wherein the cavities of biaxial framework 410 have a totalnormal dimension of 1.5″, hold an insulating material with a thermalresistivity greater than about 5.8° F.·sqft per BTUh per inch, andachieve minimum code compliance for R10ci, that is an R-value of 10°F.·sqft per BTUh of continuous insulation over the structural members.

Biaxial framework 410 has cavities that are similar in width to thewidth of the chord-like features. A convention itself is a choice andother choices are possible. By convention I will take the normaldirection of an orthogonal biaxial framework, such as biaxial framework410, to parallel the direction of a line that orthogonally intersectsthe plane of each component uniaxial framework. This same convention inthe context of a manufacturing process that produces uniaxial frameworksin a first step and then joins uniaxial frameworks together into biaxialframeworks in a second step, implies that the normal axis of biaxialframeworks produced in the second step is perpendicular to the normalaxis of the uniaxial frameworks produced in the first step.

FIG. 6B illustrates such a manufacturing process whereby twointernetworking webs longitudinally oriented along the horizontaldirection x are positioned in the two spaces between three uniaxialframeworks which are also longitudinally oriented along the horizontaldirection x to form biaxial framework 410 by pressing everythingtogether along the vertical direction y. FIG. 6B also illustrates anexploded view for biaxial framework 410′ which is a replica of biaxialframework 410 but is constructed via a second conceptual grouping of thestructural parts. This conceptual grouping contrasts with the conceptualgrouping illustrated by FIGS. 7-11. Biaxial framework 410′ comprisesthree uniaxial frameworks 421, 423, 425. The pair of frameworks 421, 423are interconnected by internetworking web array 422. Internetworking webarray 422 incorporates three internetworking webs 422 a, 422 b, 422 ceach of which three internetworking web members as typified byinternetworking web members 422 a 1, 422 a 2, 422 a 3 shown in FIG. 6B.

FIG. 6C shows a biaxial framework with a 3 by 3 matrix of chords and 7web members separately formed along each chord, including a peripheralinternetworking web of peripheral internetworking web members on thefront and back of the biaxial framework. The peripheral internetworkingweb members on the front and/or back of the biaxial framework create astandoff and a layer of cavities between itself and another connectedframework apparatus or connected object.

FIG. 6D shows a biaxial framework 409. Framework 409 has the same shape,size, and cavity structure as biaxial framework 610 shown in FIG. 6A.The features of framework 610 are modeled with reference to thestructural parts of biaxial framework 410 so as to possess a 3 by 3matrix of chord-like features and a 2 by 2 matrix of web-like featureswhich are analogous to the chords, internetworking webs, andintranetworking webs of framework 610. These features can beconceptually grouped into framework-like features, internetworkingweb-like features, and intranetworking web-like features whichrespectively correspond to the frameworks, internetworking webs, andintranetworking webs described for biaxial framework 610 in thedescription of FIG. 6A. Biaxial framework 409 reduces the flow of energyalong its normal axis

, into and out of the page along a diagonal line z sloping downwardlyfrom left to right on the page, and also reduces the flow of energyalong its lateral axis

, up and down the page in the direction shown by line y. Framework 409is a biaxial framework because it reduces the flow of energy along twoaxes. FIG. 6D shows two most-direct metric through-paths for twodifferent bundles of metric paths with spans in the normal direction tostructurally insulate against energy flow from the first chord-likefeature to the third chord-like feature analogous to chords 421 a and421 e of framework 410′. FIG. 6D shows two most-direct metricthrough-paths for two different bundles of metric paths with spans inthe lateral direction for energy flow from the first framework-likefeature to the third framework-like feature. The first and thirdframework-like features of framework 409 are analogous to the firstuniaxial framework 421 and third uniaxial framework 425 of biaxialframework 410′. These metric paths for biaxial framework 409 are similarto the metric paths for biaxial framework 410 and 410′ becauseframeworks 409 and 410 have the same shape and size. The path length ofall of these metric paths is calculated as the cumulative length of allpath segments between the start point, intermediate points, and endpoint which are shown as circles along each of the paths.

FIG. 6E shows an embodiment of a biaxial framework wherein theinternetworking web members, running between structural members in thevertical y direction, are offset in the longitudinal direction

relative to the intranetworking web members. The intranetworking webmembers being the web members that run between structural members thetransverse z direction. This configuration is advantageous formanufacturing frameworks wherein the structural members are fingerjointed together because the joints internetworking web-members fall atdifferent locations than the intranetworking web-members.

FIG. 6H shows uniaxial framework 415 and 425 without the otherstructural parts in order to reveal the structure.

FIG. 6I conceptually illustrates the transformation of uniaxialframework 415 or 425 into solid 415′ or 425′, respectively which is auseful process for other disclosed embodiments. Solids 415′ and 425′ arecontrols used to illustrate the process and represent part of anembodiment for which uniaxial framework 415 or uniaxial framework 425 isreplaced by solid 415′ or solid 425′ in framework 410 or 410′,respectively.

Other embodiments of the frameworks shown in FIGS. 6A-6K have (1) webmembers with circular, hexagonal, octagonal, polygonal, Nsp-pointed starwhere Nsp is an integer, or other shaped cross sections, (2) Niwinternetworking webs per internetworking web array where Niw is aninteger.

FIGS. 7-11 show non-limiting examples of frameworks and internetworkingwebs that can be used to build the biaxial frameworks of FIG. 6A andFIG. 6C. FIG. 7 shows a uniaxial framework 411 which is the first partof the biaxial framework 610 shown in FIG. 6A according to the firstconceptual grouping. Uniaxial framework 411 includes 4 intranetworkingweb members 438, 440, 442 and 444 that form the first intranetworkingweb between the first chord 430 and the second chord 432. Uniaxialframework 411 also includes three intranetworking web members 446, 448,450 that form a second intranetworking web between the second chord 432and the third chord 434. Intranetworking web members 446, 448, 450 arelongitudinally offset from the 4 intranetworking web members 438, 440,442 and 444 by a distance equal to half the distance betweenintranetworking web members 438 and 440. FIG. 8 shows uniaxial framework411 for reference and internetworking web array 412 which is the secondpart of the biaxial framework 610 shown in FIG. 6A according to thefirst conceptual grouping. Internetworking web array 412 comprises 18internetworking web members extending in the transverse z direction.Internetworking web array 412 connects uniaxial framework 411 touniaxial framework 413. The combination of uniaxial framework 411 andinternetworking web array 412 also constitutes an embodiment of auniaxial framework with a peripheral web array. FIG. 9 showsinternetworking web 412 a which typifies all three of theinternetworking webs in the internetworking web array 412. Each of thethree internetworking webs incorporates six internetworking web memberstypified by the web members of internetworking web 412 a. the webmembers of internetworking web 412 a correspond to the branches of thelead line for internetworking web 412 a. FIG. 10 shows internetworkingweb array 414 which is the fourth part of the biaxial framework 610shown in FIG. 6A according to the first conceptual grouping.Internetworking web array 414 connects uniaxial framework 413 touniaxial framework 415. FIG. 8 shows uniaxial framework 413 forreference. The combination of uniaxial framework 413 and internetworkingweb array 414 also constitutes an embodiment of a uniaxial frameworkwith a peripheral web. Internetworking web array 414 comprises 18internetworking web members that all extend in the same directiontransverse to the plane of uniaxial framework 413 outwardly from thepage along a diagonal line sloping downwardly from left to right on thepage. Pressing together framework 411, internetworking web array 412,framework 413, internetworking web array 414, and framework 415 producesframework 410 shown in FIG. 6A. Pressing together internetworking webarray 412, framework 411, internetworking web array 412, framework 413,internetworking web array 414, framework 415 and internetworking webarray 414 produces the biaxial framework in FIG. 6C.

FIG. 12A discloses a triaxial window frame 700 comprising four biaxialframeworks 710, 720, 730, 740 similar to that shown in FIG. 6A. Triaxialwindow frame 700 structurally insulates in the horizontal x12, verticaly12, and transverse z12 directions, that is, a direction parallel to theplane of the frame, shown as x12 with FIG. 12A, and in a directionperpendicular to the plane of the frame, shown as y12 in FIG. 12A. Insummary the triaxial window frame 700 structurally insulates in anydirection perpendicular to any of the component biaxial frameworks. Theembodiment shown in FIG. 12A includes first, second, and third sheets751, 753, 755 of material within the inner perimeter of window frame700. Each of first sheet 751, second sheet 753 and third sheet 755 maybe rigid sheets such as glass, acrylic, plexiglass, polycarbonate,polymer, crystalline solid, sapphire, diamond or a non-rigid sheet ofoptically transparent material such as window film, insulating windowfilm, acetate, polyester. In embodiments using non-rigid material, thenon-rigid material is preferably stretched across one of the sub-frames701, 703, and 705 and possibly shrunk with application of heat so as tobe taught and free of creases. In other embodiments (not shown) each ofthe sub-frames 701, 703, and 705 holds more than one sheet of material.In some embodiments like the one shown in FIG. 12A sheets 751, 753, 755and any other sheets comprise an optically transparent material or anoptically transparent but light-diffusive material. In variations of theprior embodiments, the sheets have a coating such as a security film, UVprotection film, low-emissivity coating on any of the front and/or backsurfaces of any additional sheets as well as on the front and/or backsurfaces 751′, 751″, 753′, 753″, 755′, 755″ shown in FIG. 12D of sheets751, 753, and 755, respectively. In a preferred embodiment for maximumdurability and strength the sheets 751, 753, 755 and any otheradditional sheets are made of a rigid material. In a preferredembodiment for durability with reduced weight, the outermost sheets aremade of a rigid material, i.e. sheets 751 and 755 in embodiment 700illustrated in FIG. 12A. The window frame 700 shown in FIG. 12A canfunction as a picture window or a window sash as non-limiting examples.The window frame 700 comprises four biaxial frameworks, including firstframework 710, second framework 720 (not shown and only labeled here inthe text for reference), third framework 730, and fourth frameworks 740.First framework 710 and second framework 720 are oriented vertically andjoined together by third framework 730 and fourth framework 740 whichare oriented horizontally. The first and second panes 751, 753 arepositioned next to each other forming a cavity that can be filled with agas, preferably an insulative gas. The second and third panes 753, 755are positioned next to each other forming a cavity that can also befilled with a gas, preferably an insulative gas. The second verticalframework has been removed to show the internal part of the window frame700. Each framework is a 3 by 3 framework formed by joining 3 uniaxial/1D frameworks, each of which comprises an array of 3 chords. Forinstance, framework 710 comprises three uniaxial frameworks, i.e.,uniaxial frameworks 711, 713, and 715 which each respectively comprisean array of 3 chords, {711′, 711″, 711′″}, {713′, 713″, 713′″}, and{715′, 715″, 715′″} which are labeled here in the text but not in FIG.12A to preserve visual clarity of the illustration. To illustrate thecomposition of a uniaxial framework FIG. 12A shows the array of chords{721′, 721″, 721′″} which constitute uniaxial framework 721. Uniaxialframeworks 711, 713, and 715 are connected by internetworking webs 712and 714, not labeled to avoid clutter but exemplified in the FIG. 12A byinternetworking web members 712′ and 714′, to form biaxial framework710. Each component biaxial framework 710, 720, 730, 740 structurallyinsulates along its own normal direction

and its own lateral direction

. In the illustrated embodiment, the ends of the frameworks are cut on adiagonal and joined together with miter joints in the corners. Eachchord to chord joint can be a miter joint, spline joint, butt joint,biscuit joint, mortise-tenon joint, half-lap joint, bridle joint, dadorabbet joint, dovetail joint, finger joint, or any other known type ofjoint. The component frameworks are joined such that chord in like chordlayers are joined together. Then energy will flow around the cornersinstead of running out the end of any chord in any given componentframework. In contrast, solid window frames present thermal bridges inall three spatial directions. In this embodiment, the corners havethermal bridges in that the web members in an adjacent layer are notoffset. One of the two web members at each corner, like the one labeled714′ in the upper left corner of window frame 700, is a temporary webmember that is added to preserve the form of the frame during shippingand then removed during installation to remove the thermal bridge andimprove energy efficiency. This configuration can be further modified byadding to the front or back side a 4^(th) 1D framework that has 3chords, and a fourth pane of glass. Frame 699, another embodiment ofwindow frame 700 not shown but labeled here in the text for reference,has no panes of glass and forms a frame for an opening that structurallyinsulates in all directions x12, y12, z12. Such an opening frame caninstall in a larger framework such as the wall framework 827 shown inFIG. 13A. Such an opening frame could function as a door frame, portalframe, sash for a window, casement for an operable window, conduit for apenetration, tunnel through a wall, utility chase, two-way flange formounting insulated shafts on either side, the structural frame of abuilding, etc. Such an opening frame could comprise three frameworks asshown in FIG. 12A but turned such that the longitudinal direction

720 of framework 720 aligns with the vertical axis

710.

FIG. 12B shows the embodiment of FIG. 12A with side molding or sheathing760 around the outer perimeter of the window frame 700 which can alsoapply to frame 699. The sheathing 760 is preferably an insulatingmaterial. Sheathing 760 can also be a veneer or film for example as ameans of sealing the sides against the infiltration or exfiltration ofgas from inside the cavities of frame 760. Some variants of frame 699and 700 have sheathing on the inner perimeter 760′. Other embodimenthave no sheathing on (A) the outer perimeter, (B) the inner perimeter,and/or both A and B. In other embodiments the cavities between thestructural parts of frame 699 and 700 are filled with material. Thismaterial is preferably insulating. When the insulating material is a gasthen the cavities between the sheets 751, 753, 755 and any additionalsheets can be filled along with the cavities between structural parts ofthe framework. When the outer perimeter of the framework does not havesheathing or the sheathing does not prevent the infiltration orexfiltration of gas then the fill material can provide a means ofsealing against the infiltration/exfiltration of gas through thecavities. Sealant can be applied to seal around the edges of sheets 751,753, and 755 and any additional sheets. Sheets can interface with anormal face of a structural member near the edge of the sheet asillustrated by interface 759 shown in FIG. 12C. Structural member 735′has a groove at interface 759 which provides a seat on which sheet 755sits. The groove also provides a bed for sealant when sealant is appliedbefore seating sheet 755. Any structural member with a groove likestructural member 735′ can have no groove like structural member 733′ asshown at interface 757 in FIG. 13C. For this type of interface the sheetand/or sealant rests on the inner lateral face of structural member733′. A groove can be created for interface 757 without removingmaterial by adding a spacer to the inner lateral face of structuralmember 733′. Frame 699 and 700 could have muntins. Non-structural orstructural, insulative muntins can be incorporated using the samemethods described for window frame 700. Frame 359 in FIG. 36EAincorporates a structurally insulative muntin in the form of uniaxialframework 360′ that runs horizontally. In some embodiments the fourframework 710, 720, 730, and 740 form a four way cross. The describedmethod of joinery can also be used to construct elbows, tees, four-waycrosses, planar grids, six-way crosses, and spatial grids (not shown).At interface 755 a single structural member in one uniaxial frameworkjoins with a pair of structural members in another uniaxial framework.Any of the front facing uniaxial frameworks and any of the back facingframeworks in frame 700 can be solid as illustrated by thetransformation of framework 425 shown in FIG. 6H into solid 425′ shownin FIG. 6I. Although the resulting embodiment no longer structurallyinsulates directly through the solid portions, the interior uniaxialframeworks still structurally insulate the remainder of frame 700.

Biaxial frameworks 710, 720, 730, and 740 may also have molding orsheathing on the outward front normal surfaces. The sheathing could belike that of the side sheathing. The sheathing is visible when installedand could be for decoration. In a preferred embodiment for excellentinsulative performance the sheathing is an insulative material. Inembodiments, the side molding 760 includes two vertical components 761,763 and two horizontal components 762, 764. In embodiments the frontmolding 765 is formed around all four sides of the front side 700′ ofthe window frame 700, and the back molding 765′ (FIG. 12D) is formedaround all four sides of the back side 700″ of the window frame 700.FIGS. 12C and 12D show the window frame 700 from the opposite side. FIG.12D shows an embodiment of frame 700 with sheathing.

FIG. 12E discloses frame 780, a uniaxial variant of triaxial frame 700,that structurally insulates in the normal direction coinciding with thetransverse z direction in the figure. The framework 780 comprises threethin frames 781, 783, and 785 that are stacked in the transverse zdirection. The first thin frame 781 is a combination ofstructural-members 781′, 781″, 781′″, and 781″″. Embodiments of frame780 can have any of the variations mentioned for opening frame 699. Forinstance, frame 780 can incorporate sheathing. By discretizing any fullrotation around an intrinsic angle into N discrete angles, which are notnecessarily evenly spaced, one can conceptually create a framework inthe shape of an N-sided polygon or any portion of an N-sided polygon.For example, a four-step rotation in orbital pitch angle structuralmember 781′ produces the elements 781″, 781′″, and 781″″ and the wholeframe 781 as a single part rather than a collection of four parts inFIG. 12E. For example four-step rotation in orbital yaw angle of thestructural parts 781′, 782′, 783′, 784′, 785′ produces a functionalequivalent of whole framework 780 as a single part rather than acollection of 20 parts. One can build the same window framework 780 byapplying a four-step rotation in orbital yaw angle of the structuralmembers 781′, 783′, and 785′, placing web-members 782′, 782″, 782″,782″″ between reference frames 781 and 783 with an even spacing beingpreferred, and then placing the web-members 784′, 784″, 784″, 784″″between reference frames 783 and 785 so that they are offset fromweb-members 782′, 782″, 782′″, 782″″ with a preference toward orbitalyaw angles half way between those of web-members 782′, 782″, 782′″,782″″. Additional constraints such as structural integrity at the jointsand aesthetic design can alter the preferred orbital yaw angle of theweb members. Another embodiment of framework 780 has an octagonal shapeproduced by eight-step rotation of structural parts 781′, 782′, 783′,784′, 785′. This same conceptual process applies to any embodiment notjust framework 780. One can start with a biaxial framework like biaxialframework 730. For instance, four-step rotation in orbital yaw angle ofbiaxial framework 730 produces multiaxial framework 700. The mitered endconditions of the structural members in framework 730 give a differentaesthetic than the un-mitered ends of the structural members offramework 780. Given a particular embodiment one can infer how manydiscrete steps in angle are used for rotation. A number N steps can beapplied to rotation of structural members and a different number M stepscan be applied to rotation of web members. An offset is applied toweb-members in one of two adjacent webs.

FIG. 12F discloses window frame 780′ with first, second, third, fourth,fifth, and sixth sheets 791, 792, 793, 794, and 795 of material withinthe inner perimeter of window frame 780. Each sheet noticeably reducesthe convective transfer of heat between the outermost sheets which aresheets 791 and 796 for the embodiment shown in FIG. 12F. Any sheetincorporated into window frame 780′ or window frame 700 could be anumber of thinner sheets pressed together. Other embodiments have fewerthan six sheets. For instance, window 2963, built for testing, has fivesheets in the form of glass panes. Other embodiments have more than sixsheets, more than three structural members, and more than two webs ofweb members. Embodiments of window frame 780′ can have any of thevariations mentioned for window frame 700. For instance, window frame780′ can also serve as a window sash, a casement for a casement window,and the like. Any variations mentioned here also apply to windows 700and 840′. In embodiments of windows 700, 780′, and 840′ the spacebetween each pair of sheets is filled with an insulative gas. Inembodiments of windows 700, 780′, and 840′ preferred for energyefficiency, the space between each pair of sheets is filled with aninsulative gas with molecular weight greater than that of air in orderto slow the convective flow of heat between the sheets 751, 753, 755,791, 792, 793, 794, 795, 796, 851, 852, 853, 854. In embodiments ofwindows 700, 780′, and 840′ preferred for reducing convection andreducing radiative heat loss and radiative heat gain through the window,the space between each pair of sheets is filled with a greenhouse gaswith a molecular weight greater than that of air. The greenhouse gasbeing for example carbon dioxide, methane, or any other gas that absorbssolar radiation. The greenhouse gas works to absorb incoming radiationand then reradiate the energy into all directions with approximately 50%of the incident radiation being reradiated backward to some extentrelative to the incident direction. In the heating season the greenhousegas works to prevent heat loss from the building in which the window isinstalled by absorbing and reradiating incident radiation back into thebuilding. In the cooling season the greenhouse gas works to activelyreject infrared and visible radiation produced by the sun andsurrounding objects. Any other gas with a large molecular weight and/orabsorption line in the visible or infrared spectrum could be usedinstead. Experimental window 2963 shown in FIG. 36H was filled withcarbon dioxide gas using dry ice and the process of sublimationaccelerated to generate the carbon dioxide gas. Experimental window 2963used window frame 708′. A greenhouse gas can also serve as a filler foranother embodiment of the present invention. Furthermore, a greenhousegas could also be used to fill apparatuses that do that do notincorporate an insulatable, insulative framework such as an insulatingglass unit, a window, a wall cavity, or other type of air-sealedframework.

FIGS. 12G, 12H, and 12I each illustrate an embodiment incorporating fouruniaxial frameworks and a different method of joining the four uniaxialframeworks together into a rectangular frame. FIG. 12H illustrates amethod of joining the four uniaxial frameworks by joining eachstructural member in one framework to another structural member in alike layer of another framework. Instead of joining single structuralmembers one can join a pair of structural members in one framework to asingle structural member in another framework as illustrated byinterface 755 in FIG. 12G. The method of joinery illustrated by FIGS.12G and 12H creates a unified structure with the same the structuralinsulation factor as the component frameworks as measured along the mostdirect metric path in a direction perpendicular to the structuralmembers. FIG. 12H illustrates an embodiment of joining uniaxialframeworks. The method of joinery illustrated by FIG. 12H creates aunified structure with a lesser structural insulation factor than thatof the component frameworks, as measured along the most direct metricpath in a direction perpendicular to the structural members. However,this method of joinery might be preferred for expediency as anon-limiting example.

FIGS. 12F and 12G disclose a structurally insulative frame 840 andstructurally insulative window 840′ each of which incorporates fouruniaxial frameworks 831, 832, 833, 834. Each of the uniaxial frameworks831, 832, 833, 834 incorporates two chords 841 and 843 interconnected bya web of diagonal web members typified by diagonal web member 842. Theseweb members could have any pitch angle between 0° and ±90° relative toone of the chords 841. The web members shown have a pitch angle of 15°with an alternating positive and negative sign. In other embodiments(not shown) the web members 842 are dowels with polygonal or circularcross sections. Retainers, typified by retainer 844, provide a brace toretain diagonal web members 842 that terminate at the ends of aframework 831, 832, 833, or 834. In some embodiments structurallyinsulative frame 840 is spun 90° around its central axis running in thetransverse z direction of the figure such that the bottom framework 833would support frameworks 832 and 834. In that configuration frameworks832 and 834 can function as studs and frameworks 831 and 833 canfunction as a top plate and bottom plate or vice versa. In the currentconfiguration frameworks 831 and 833 can function as studs andframeworks 832 and 834 can function as cross braces. FIG. 12G shows acutaway view with uniaxial framework 831 omitted to more clearly revealthe edges of glass panes 851, 852, 853, and 854 which are incorporatedinto frame 840 to create structurally insulative window 840′. All of thevariations mentioned for windows 700 and 780′ apply to window 840′.

FIG. 13A shows a structure 800 that structurally insulates in threedirections. More particularly, this figure shows how uniaxial/1Dframeworks and biaxial/2D frameworks can combine to form a frame thatstructurally insulates in three directions in this case (1) upward anddownward through the foundation framework in the vertical y13 direction(2) inward and outward through the foundation framework along thenorth/south axis, transverse z13 axis, and (3) inward and outwardthrough the foundation framework along the west/east axis, horizontalx13 axis. Four frameworks, exemplified by biaxial framework 825 in FIG.13A, joined together at right angles create a framework that serves asan insulatable, insulation foundation for building walls. FIG. 13A alsodiscloses a means of constructing a wall with uniaxial/1D frameworksthat serve as studs, exemplified by uniaxial framework 812, anduniaxial/1D frameworks that serve as top plates, exemplified by uniaxialframework 816, and bottom plates, exemplified by uniaxial framework 818.The embodiment of stud-like uniaxial framework 812, illustrated in FIG.13A, and constituting each stud, has web members that are (1) the samethickness and width as the structural members and (2) spaced along thelongitudinal direction

812 with the same spacing as the web members of top-plate-like uniaxialframework 816. Stud-like uniaxial framework 812 derives strength fromthe fact that the web members are short with respect to their span inthe normal direction

812 so that applied forces have a short lever arm on which to work. Notethat any biaxial framework can benefit from the joinery method shown inFIG. 12G and 12H. Any number of floating tenons, between a web-memberand adjacent structural members can strength the framework against shearforces acting along the longitudinal direction. Note that the corners ofthe foundation framework might appear to have thermal bridges in thatthe braces in an adjacent layers are not offset. However, unlike theframework in FIGS. 12A-12D, this framework has only one edge that isexposed to the indoor environment. An entire face of the framework isnot exposed to the indoor environment as for the window frame in FIGS.12A-12D. Thus, the web members in an adjacent layer that are not offsetdo not constitute a thermal bridge. They represent a purely mechanicalbridge that strengthens the corner. FIG. 6H shows uniaxial frameworks415 and 425 that constitute the outermost uniaxial framework componentsfor biaxial framework 410. Biaxial framework 810 has a uniaxialframework 815 with its normal

axis oriented along the vertical y direction analogous to framework 415and has a uniaxial framework 825 analogous to framework 425 with itsnormal

axis oriented along the transverse z direction. In an embodiment (notshown) vertical uniaxial framework 815 is a solid board with the sameenvelope dimensions as framework 815 in order to provide additionalstrength and function as a rim joist for mounting other structures likea deck. In an embodiment (not shown) horizontal uniaxial framework 825is a solid board with the same envelope dimensions as framework 815 inorder to provide additional strength and function as a sole plate tofasten down to a sill plate, j-bolts, or similar means of connectingframework 810 with any additional portion of the foundation which mightinclude a masonry wall, concrete wall, concrete slab, pier system, solidtimber frame, as non-limiting examples. In an embodiment (not shown)both vertical uniaxial framework 815 and horizontal uniaxial framework825 are solid boards configured as in the prior two embodiments inanalogy to FIG. 1 which shows frameworks 415 and 425 as solid boardswith the same envelope dimensions as frameworks 415 and 425.

In FIG. 13A, the lower portion 805 of the structure 800 is formed from atotal of four biaxial framework segments, like biaxial framework 810,connected to form a rectangle, that resist heat flow in the directionsthat are not parallel to the length of the chords. Each of the fourbiaxial framework segments include three uniaxial frameworks and threestructural members per uniaxial framework for a total of nine structuralmembers. In the south east corner of lower portion of foundation 800lower portion 805 Another embodiment includes uniaxial frameworkstypified by uniaxial framework 820 running in the horizontal directionbetween two opposing biaxial frameworks of lower portion 805 whichfunction as structurally insulative joists in embodiments of structure800. The vertical portion 827 of the structure 800 is formed from seven1 by 3 uniaxial framework segments 812 that resist heat flow in thedirection z13, which is perpendicular to the plane of the frameworkportion 827 and function as studs in embodiments of structure 800. Theseseven segments 812 are connected across their bottom terminal ends touniaxial framework 818, which serves as a bottom plate for the wall, andare connected at the top to uniaxial framework 816, which serves as atop plate, across their top terminal ends. In one embodiment of abuilding method the entire vertical portion 827 is assembled lying downon a horizontal surface and then stood up into position as often done inconventional stick framing. The reduction in weight afforded by thecavity structure of each framework in the vertical portion 827 has theadvantage of (a) reducing strain and injury on workers, (b) easing theprocess of raising the vertical portion 827 into position, and (c)enabling larger wall sections to be constructed when the total weight ofvertical portion 827 is comparable to that of a conventional wall frame.In another embodiment (not shown) sheathing, wrap, or other surfacedefining means is applied to the interior and exterior surfaces of thestructure 800 to create fully enclosed cavities which are filled with aninsulating material to block convective flow of gas trapped within theenclosed cavities caused by temperature differences across the wall orheat from a fire and block the conductive flow of energy through theenclosed cavities including those of the framework members. The threechords of each uniaxial framework segments 812 enhance structuralreliability, for instance, by (1) avoiding sudden failure if any one ofthe three chords is compromised by fire, chemicals, projectile,shockwave, earthquake, hurricane, or other attack and (2) increasing thetime until failure under sustained conditions of attack in theaforementioned scenarios relative to two-chord embodiments. Anotheradvantage is that the binary connections between each web member andeach structural member mean that the structure is determinate for astructural engineering analysis. Another embodiment includes a web orhorizontal web members that connect adjacent uniaxial framework segments812 into a lattice similar to the one shown in FIG. 35A. This embodimentmay further increase the time until failure during a fire especiallywhen insulated with a fire resistant insulative fill material such asmineral wool or borated cellulose insulation such that fire burns alongthe most direct metric path.

FIG. 13B shows a close-up view of the south east corner of structure 800shown in FIG. 13A. This framework is a smaller biaxial framework whichis inserted into the larger biaxial framework 825 to strengthen thecorner.

FIG. 14 shows a cylindrical tube-shaped triaxial structure 910 thatincludes first, second and third circular frameworks 913, 915, 917 ofconcentric, coaxial first, second and third circular chords 930, 932 and934, with each circular framework being vertically spaced from theothers along a common vertical axis and being parallel to the others.The circular structural members and web member between them areintegrally formed. In other embodiments the web members and circularstructural members separate sets of structural parts joined together.This configuration structurally insulates along (a) the axial directionof the cylindrical framework and (b) the radial direction whichencompasses both the horizontal and transverse directions. In summarythe triaxial structure 910 structurally insulates along anyperpendicular to the chords. This is a variation of FIG. 6A. Theconfiguration can be modified to include (a) fewer concentric chords, or(b) additional concentric chords, and/or (c) fewer vertically spacedcircular frameworks, and/or (d) additional vertically spaced chord sets.In the embodiment shown in FIG. 14, the concentric chords have a spacingthat is similar to the thickness of the individual chords, however,other embodiments (not shown) have smaller relative spacing and largerspacing relative to the thickness of the individual chords. The spacingbetween first and second chords can be the same as, or different from,the spacing between third and fourth chords as a non-limiting example.In the embodiment shown in FIG. 14, the distance between verticallyspaced chord sets is about 4-5 times the thickness of the individualchords to provide a substantially non-zero span-wise indirectness in thevertical direction and to better illustrate the internal structure ofthe circular frameworks. However, smaller or larger spacing can be used.Smaller spacing yields greater span-wise indirectness and greater valuesof structural insulation factors in the vertical direction as well asthe radial direction. In the embodiment shown in FIG. 14, thehorizontally extending web members 936 are spaced such that there arefour horizontally extending web members between adjacent pairs onconcentric chords at a given height. The appropriate spacing between webmembers can be inferred by scaling the dimensional parameters in Table 2and then using them as arc lengths for around the circumference of acircular structural member. The arclength spacing can also be calculatedusing the equations in Table 2 and working backwards from the targetedstructural insulation factor, F_(target), corrected for the effects ofnon-isotropic resistivity along metric paths in the targeted directionto solve for the spacing which relates to the length along the metricpath. For example, referring to the metric path diagrammed in FIG. 2AIfor the three-chord framework shown in FIG. 2AH, the spacing Δ

approximately equals L−{Δ

1001+Δ

1002+Δ

1004+Δ

1005} where L equals F_(target)·S. In this case the spacing the spacingΔ

corresponds to an arclength rather than a linear length. To understandthis idea wrap uniaxial framework 1000, shown in FIG. 2AH, into acircle. Alternatively imagine cutting one of the circular structuralmembers and straightening it out. Finally, one can rework the equationsin table 2 for arclength and do the calculation directly in cylindricalcoordinates. Similar ideas hold for calculating the spacing of webmembers in the vertical directions (axial direction). In the embodimentshown in FIG. 14, the vertically extending web members 938 are spacedsuch that there are four vertically extending web members betweenadjacent sets of the outermost chords and four vertically extending webmembers between adjacent sets of the innermost chords. In otherembodiments there also are vertically extending web members positionedbetween adjacent intermediate chords in analogy to the biaxial frameworkshown in FIG. 6E. In other embodiments there are vertically extendingweb members positioned between only adjacent intermediate chords inanalogy to the biaxial framework shown in FIG. 6J. The embodiment offramework 910 shown in FIG. 14 corresponds to bending a slightly longerembodiment of the biaxial framework shown in FIG. 6K with additional webmembers around an orbital pitch axis such that the ends of the biaxialframework wrap around and join with each other end to end. Otherembodiments of triaxial frameworks can be created by bending any biaxialframework like those shown in FIGS. 6A-6K in the orbital yaw axis,orbital pitch axis or any other orbital axis that allows the structuralmembers to wrap around and join end to end. Framework 910 in FIG. 14represents an embodiment of ˜20-step rotation in orbital pitch angle ofthe structural members and 4-step rotation in orbital pitch angle of theweb members. An offset of 45° is applied to rotation in orbital pitchangle for the outermost web of each uniaxial framework. This figurepractically illustrates continuous rotation of infinitely shortstructural members but does not exactly illustrate continuous rotationalextrusion of a cross section of structural members because the 3D CADsoftware is not capable of modeling continuous curves, that is,non-discretized curves. Continuous rotation along a first spin axis of aspin-symmetric array of structural-member cross sections createsconcentric structural shells. These structural shells can bestructurally insulated by discrete-step rotation, around the same spinaxis but in orbital angle, of web-member cross sections with web-membersin adjacent webs having a different angular offset. Further continuousspin rotation of the structural member array along an orthogonal spindirection creates completely closed concentric structural cells. Thesestructural shells can be structurally insulated by discrete orbitalrotation, along the orthogonal spin direction, of web-member crosssections with web-members in adjacent webs having a different offset inorbital angle. All internetworking web members could be solid cylindersbut are shown here to (a) reveal the internal structural (b)structurally insulate along the axial direction and (c) create atriaxial framework.

FIG. 15 shows an embodiment of a multiscale, biaxial framework 1500. Inthis embodiment, the chords 1501, 1503 and 1505 are each made from astack of frameworks 1510, and each web member 1502 is made from a stackof frameworks 1512. More specifically, in the illustrated embodiment,each chord is made from a stack containing about 50-60 frameworks, andeach web member is made from a stack containing about 5 frameworks.Larger or smaller number of frameworks can be used in the stacksdepending on the desired size and strength of multiscale, biaxialframework 1500. Multiscale, biaxial framework 1500 structurallyinsulates in the longitudinal direction (the vertical y direction inFIG. 15) and the normal direction (the horizontal x direction in FIG.15). In the version shown in FIG. 15, the frameworks in the chord stackextend horizontally and the frameworks in the web member stack extendvertically.

FIG. 16 shows triaxial framework 1600 made from three aligned frameworks1601, 1602 and 1603. The web members 1602 are staggered relative to webmembers 1604. In both sets of web members 1602 and 1604 each web memberextends across two out of the three aligned frameworks. Triaxialframework 1600 is a multiscale framework made with web members andchords that are small frameworks in and of themselves. One can create anembodiment with any arbitrary number of scales by making the structuralparts at any given scale into small frameworks in and of themselves.Likewise, one can create an embodiment with any arbitrary number ofscales by making the structural parts into a larger structurallyinsulative framework. Triaxial framework 1600 structurally insulates inall three directions, i.e. the longitudinal direction along the longaxis of the framework (transverse z direction in the figure), normaldirection (horizontal x direction in the figure), and lateral direction(vertical y direction in the figure). This framework reduces energy flowin the vertical direction with a similar geometry to that of theframework disclosed in FIG. 17. The front layer of three strut-likestructures and front layer of four web members 1602 constitutes a singlelayer biaxial framework that suppresses energy flow along the transversez direction in the picture and the vertical y direction in FIG. 16. Inanother embodiment shown in FIG. 26 of U.S. Provisional PatentApplication No. 62/720,808 the general cross sectional shape of thechords is square rather than rectangular.

FIG. 17A illustrates an embodiment of a laterally extended framework ofstructural formations as a building panel 1206 with vertical stud-likeframeworks 1210. Framework panel 1206 also includes a rigid, planarsolid board 1270, and horizontal strapping 1272. Insulatable frameworkpanel 1206 structurally insulates along the transverse z17 directionperpendicular to the plane of the board 1270. Framework panel 1206contains three structural formations 1270, 1211, and 1212. Structuralformation 1270 is the board 1270. Structural formations 1211, 1212 eachincorporate three chords that are not directly connected and are spacedapart in the horizontal x direction as shown in FIG. 17B. The branchesof the lead line labeled 1211 correspond to individual chords in thestructural formation 1211. The branches of the lead line labeled 1212correspond to individual chords in the structural formation 1212. Eachpair of structural formations is interconnected by one of the webformations 1214, 1213. Each of web formations 1213, 1214 contains 3webs. Each of the 3 webs in each of the web formations 1213, 1214contains six web members. Each of the three branches of the line labeled1213 in FIG. 17B points to the first web member in each of the threewebs that constitute web formation 1213. Each of the three branches ofthe line labeled 1214 in FIG. 17B points to the first web member in eachof the three webs that constitute web formation 1214. In otherembodiments (not shown) each chord is an array of structural memberssuch as a group of veneer strips laminated together. In otherembodiments (not shown) each structural formation is an array ofstructural formations such as a multiplicity of framework panelsconnected together either using the present methods or not using thepresent methods. As a non-limiting example, using the present methods toconnect such an array of framework panels can provide protection againstthe lateral spread of fire between structurally connected frameworkpanels that form an insulatable, insulative wall framework apparatus.

FIG. 18 illustrates an embodiment of an insulatable, insulative buildingpanel 1800 comprising a lattice framework 1812 between two sheets 1815,1817 which serve as sheathing to contain insulating material as well asblock convective and radiative transfer in the normal

direction (vertical y direction in the figure). Different embodiments ofsheets 1815, 1817 are rigid while others are flexible. Differentembodiments of the two sheets 1815, 1817 are structural while others arenon-structural. Different embodiments of the two sheets 1815, 1817 aretransparent while others are semi-opaque or opaque. Two layers ofstructural members 1836 run in the transverse z direction in the figure.Structural members 1836 in different layers are offset in the horizontalx direction of the figure. Web members 1834 in different layers areoffset in the transverse z direction of the figure. Two layers of webmembers 1834 run in the horizontal x direction in the figure and joinwith the structural members to create the lattice framework 1812.Framework 1812 structurally insulates along its own normal

₁₈₀₀ axis parallel to the vertical y direction. To conductively flowfrom the bottom sheet 1815 into a structural member 1836 and then to thetop sheet 1817 along the vertical y direction, energy must additionallyflow in the transverse z direction, then in the horizontal x direction,and then again in the transverse z direction along the way. Toconductively flow from the bottom sheet 1815 into a web member 1834 andthen to the top sheet 1817 along the vertical y direction, energy mustadditionally flow in the horizontal x direction, then in the transversez direction, and then again in the horizontal x direction along the way.The top layer of sheathing 1817 is partially cut away in order to bettershow the underlying structure. One layer of sheathing or both layers ofsheathing could be omitted.

FIG. 19 illustrates one embodiment of the framework as an insulativepanel 1900 comprising three or more sheets 1912, 1914, and 1916 ofmaterial with two or more layers of spacer ribs 1918 staggered relativeto those of the adjacent layer. In some embodiments of panel 1900 thesheets are made of transparent material and together function as atriple-pane window 1900 with a scarf joint. The illustration shows onesheet of material offset from the other. This design allows multiplepanels to scarf-join together and maintain their full insulativecapability. The illustration shows a transparent material that allowsone to better see the structure.

FIG. 20A illustrates on embodiment of the framework demonstrating how tomake and use a scarf joint to longitudinally connect together biaxialframeworks 1612, shown separately in FIG. 20B, and 1614, shownseparately in FIG. 20C. In the embodiment shown, each framework hasnominal exterior dimensions of 4 inch by 8 inch (100 mm×200 mm) alongthe non-longitudinal axes. This figure also illustrates the requiredconfiguration for the ends of the chords. In some cases, theseframeworks are made of wood. A worker can glue these frameworks togetherin the field. The protruding blocks, typified by block 1616 in FIG. 20C,lock the two frameworks together along their normal and lateral axes.Holes drilled through overlapping pieces of the frameworks filled withpins made from wood dowels or any other material can further secure thetwo frameworks together along their longitudinal axes. Nails or screwsdriven through overlapping pieces of the frameworks could serve the samethe purpose. This same method also works for uniaxial frameworks. FIG.20A also illustrates this concept. For instance, the foreground set ofchords and web-members 1622, 1624 for halves 1612 and 1614,respectively, constitute uniaxial frameworks and shows how they can bescarf joined. FIGS. 32 and 34 in U.S. Provisional Patent Application No.62/720,808 show other embodiments of scarf joined biaxial frameworks.

FIG. 21 shows an elevation view of a uniaxial framework 1712 thatstructurally insulates along its normal axis (into and out of the pagealong a diagonal sloping downward from left to right on the page) andmost-direct metric through-paths 1721 and 1723 from two differentbundles of metric paths with a span in the normal direction.

FIG. 22A illustrates one embodiment of a vertically extending uniaxialframework filled with insulating material. The framework has protrusionswhich provide space, typified by cavities 5 a and 5 b, for insulationbetween the nearest chord-like feature and the interior facing surfaceof any cooperative object attached to the protrusions. One exampleprotrusion contains the points labeled 5 c and 5 d in FIG. 2A. Thepoints 5 c and 5 d are the starting points for two most-direct metricthrough-paths from two different bundles of metric paths with a span inthe normal direction. The protrusions also significantly increase thelength of the two most-direct metric through-paths shown relative towhat they would be in the absence of protrusions.

FIG. 22B magnifies the dotted-line region of FIG. 22A and showsintermediate points 6 b, 6 a′ as well as end point 5 c′ for the pathbeginning at 5 c. FIG. 22B also shows intermediate points 7 b, 7 a′ aswell as end point 5 d′ for the path beginning at 5 d. The path length ofeach path is calculated as the cumulative length of all path segmentsbetween the start point, intermediate points, and end point.

FIGS. 23A and 23B show two different configurations of a stud and platejoined together with a screw and a nail. In FIG. 23A the web member 2304of plate-like framework 2314 extends into the cavity created by a pairof structural members in stud-like framework 2311 lying down as it wouldbe when framing a wall for instance. FIG. 23A shows a screw driventhrough the pair of structural members and web member 2304. However, adowel, nail, or any other appropriate fastener could be used instead ofthe screw. This type of connection is preferred for strength over theother connection show in FIG. 23A in which a nail is driven throughchord 2301 of the plate-like framework 2314 into the adjacent chord ofstud-like framework 2311. Web member 2302 is shown with a dotted line toindicate that it is not in the same plane as web member 2304. Thisconvention is used in other figures as well. Thus, the web members 2302and 2304 are offset and provide no direct path for conductive energyflow between chords 2305 and 2301 through chord 2303 of framework 2300.Furthermore, the greater the offset between web members 2302 and 2304the more indirect the most-direct metric path through them becomesmaking the structural insulation factor larger. In FIG. 23B web member2314 of framework 23B extends into a cavity created by chords 2305 and2303 of framework 2300. Then frameworks 2300 and 2310 are securedtogether with a screw driven through chords 2305 and 2303 and web member2314.

FIGS. 24A and 24B <.F040, page 22, original FIG. 40 on page 35.>illustrate a uniaxial framework 2400 comprising laminations 2410, 2411,2412, and 2413. Framework 2400 is rotated in FIG. 24B relative to thatin FIG. 24A to show the opposite side as indicated by the axis labely2400. Laminations 2410 and 2412 build to form chords. Laminations 2412run the entire length of framework 2400. Additional laminations likelaminations 2412 could be added to make an I-beam cross section andstrengthen the overall framework. Laminations 2410 run betweenweb-member-like laminations 2411. Web-member-like laminations 2413 runbetween chord-like laminations 2412. In order to manufacture framework2400, one could assemble the laminations into a form with theorientation of the framework in FIG. 21. Then the laminations could bepressed together. Heat could be applied conductively through the formand faces of the press. Heat could also be applied via radiative heatingwith microwaves or other suitable form of radiation. Other embodimentsuse laminations characteristic of oriented strand lumber, crosslaminated timber, parallel strand lumber, or laminated strand lumber.The laminations 2410, 2411, 2412, and 2413 shown in FIG. 24 arecharacteristic of laminated veneer lumber. The laminations could beprepressed with or without heat before being fully pressed together intofinal form. Frameworks can also be glued together in the configurationshown in FIG. 6 of U.S. Provisional Patent Application No. 62/720,808.Frameworks can be manufacture by creating a wide framework as shown inFIG. 6 of U.S. Provisional Patent Application No. 62/720,808 and thencutting the wide framework into more narrow frameworks.

FIGS. 25A-25D <.F044, page 23.> schematically illustrate differentembodiments and views of a structurally insulative joist framework 2512with and without straight-through, web-member braces. This set offigures shows a structure that is trimmable, insulatable, and insulativewith a portion that has two structural members and diagonal web members.A preferred embodiment, shown in 25D, for framing a barrier insulatedalong its entire length has no straight-thru braces.

FIG. 26 shows a different embodiment of a structurally insulative joistframework with straight-through braces/web-members. The structure ofFIG. 25F may be preferred when the joist need only be structurallyinsulative at its ends. In that case the straight-thru web members donot degrade thermal performance and provide space for running utilitiesfor example. The end views of FIGS. 25A, 25C and 25E show differentpossible profiles of (a) nominal 2 inch by 2 inch top and bottom chords(c) nominal 2 inch by 4 inch top and bottom chords (e) nominal 2 inch by3 inch top and bottom chords, for the apparatuses in the lengthwiseviews 25D and 25F.

FIG. 27A shows a side view of a framework pre-form 2211 that includesthree parallel chords 2230, 2232 and 2234 with a first continuous webmember 2237 extending along the length of the structure pre-form 2211between first and second chords 2230, 2232, and a second continuous webmember 2239 extending along the length of the structure pre-form 2211between second and third chords 2232, 2234. FIG. 27B illustrates an endview of the structure, showing that the web members 2237, 2239 arethinner than the chords. Openings can be cut in the web members 2237 and2239 to create indirect paths in the vertical direction on the pagebetween the first chord 2230 and the third chord 2234 in order to formthe finished structure.

FIG. 28A illustrates an end view of one embodiment of a roof frame 2306.Each end of the roof frame 2306 includes a pair of slanted beams 2353,2354 that are joined in an upside-down V configuration to form the peakof the gable. A vertical support 2357 provides reinforcement to thebeams 2353, 2354 by carrying some of the load of the roofing material.The main horizontal tie 2310 is formed from first, second and thirdchords 2331, 2333, 2335, respectively, with web members 2332 positionedbetween the first and second chords 2331, 2333, and web members 2334positioned between the second and third chords 2333, 2335. Verticalsmall frameworks 2313 and 2315 support opposite end of the mainhorizontal support 2310. Each of the vertical frameworks is made fromthree chords and two web members. Diagonal beams 2355 and 2356 providereinforcement to the center of the main horizontal tie beam 2310. Theroof framework has a main horizontal apparatus that incorporates threestructural members. Each structural member has a horizontal tie memberand a vertical heel member. The three structural members are connectedtogether by two intervening webs. Each of the webs has a plurality ofbraces. Instead of joining structural members and braces one could cutopenings into a single heel in order to create the same indirect pathsof the three braced heels. In this embodiment, the various truss membersare jointed together with metal truss plates that can be stamped to forman array of integrated nails.

FIG. 28B illustrates a roof frame 2306′ similar to that of FIG. 28A withgussets 2386, 2388, 2390, 2392, 2394 and 2396 to join the frameworkmembers together. The gussets can be glued, nailed, or attached inanother suitable manner. The gussets do not modify the minimum rangewiseindirectness of the main horizontal tie member. The broken line 2397shows a “W” shaped web that could substitute for the single verticalsupport that rises to the peak of the gable.

FIG. 29 illustrates an end view of a structure 2410 that includes a roofframe 2306″ similar to that of FIG. 28A mounted on an enclosure 2411,such as a building. The two illustrated frameworks 2412, 2414, 2416 and2418 can be uniaxial frameworks each comprising a 3 by 1 matrix ofstructural members or a biaxial framework comprising a 3 by 3 matrix ofstructural members, or can have other dimensions depending on thebuilding size and load requirements. The illustrated embodiment shows 3by 1 frameworks for ease of understanding. In the construction of abuilding, the opposite end of the building would have a similarstructure, and there would be four horizontal frameworks connecting thetwo opposite end of the building frame. Two transversely orientedtop-plate-like uniaxial frameworks 2413 and 2415 sit on top of each walland tie together the stud-like frameworks at their top ends. Atransversely oriented bottom-plate-like and sole-plate-like uniaxialframeworks sit at the base of each wall and tie together the stud-likeframeworks at their bottom ends. Uniaxial framework 2416 is afloor-joist-like framework.

FIGS. 30A-30E <.F050A, F050B, F050C, F050D, page 26 and FIG. 51.>schematically illustrate various stacked and rotated embodiments of theframework where the structural members and web members are seamlesslyconnected so that they become an integrated unit withstructural-member-like features and web-member-like features withoutjoints. FIG. 30A shows a first unit 2522 decorated with vertical stripesfor the purpose of illustration. FIG. 30B shows a second unit 2524. Thesecond unit 2524 is that same as the first unit 2522 except that it hasbeen rotated by 180° around its longitudinal axis and decorated withhorizontal stripes for the purpose of illustration. FIG. 30C shows thefirst unit 2522 stacked on the second unit 2524 and a third unit 2526,which is identical to the second unit 2524. The second unit 2524 isunderneath and to the left while the third unit 2526 is underneath andto the right. The first unit 2522 is drawn with a transparent backgroundto illustrate the positional relationship of the first unit with thesecond and third unit. The left half 2527 of the closed cavity 2528 inthe first unit 2522 lines up with the right open cavity 2532 of thesecond unit 2524. The right half 2531 of the closed cavity 2528 in thefirst unit 2522 lines up with the left open cavity 2535 of the thirdunit 2526. The right half 2533 of the closed cavity 2534 in the secondunit 2524 lines up with the open cavity 2535 on the left side of thethird unit 2526. The left half 2536 of the closed cavity 2537 of thethird unit 2526 lines up with the open cavity 2538 on the right side ofthe first unit 2522. This feature means that the first unit 2522 canform a “running bond” with copies of itself as shown FIG. 30D. Runningbonds are important for strength in a wall assembly. In FIG. 30D theinner edges 2550, 2552 of the lower units 2551, 2553, respectively, areoffset essentially half way between the inner edge 2554 of the upperunit 2556 in a “running bond” configuration. The gaps between the unitsprovide space for a substance to bond the units together. Embodiments offrameworks 2522, 2524, 2612, and 2614 take the form of bricks, masonryunits, and blocks. Embodiments of frameworks 2522, 2524, 2612, and 2614could be made from any material but ceramics, concrete, adobe, andrammed earth are commonly used materials for bricks, masonry units, andblocks. FIG. 31D shows a brick-like framework with a structurallynon-insulating cavity 2563. Cavity 2563 can be considered asstructurally non-insulating cavities because no metric path intersectscavity 2563. Structurally non-insulating web members and structuralmembers are also possible when no metric path intersects them. Cavity2563 does contribute somewhat to the insulatable aspect of the brick.Embodiments preferred for their insulatable aspects may havestructurally non-insulating cavities. Embodiments preferred for theirstrength have few to zero structurally non-insulating cavities. Features2564 and 2565 are ineffective features because the presence of features2564, 2565 do not change the insulation characteristics of the overallstructure by more than 10%. The analog of these ineffective features inthe case of a framework made of structural parts would be ineffectiveweb members and structural members whose presence does not change theinsulation characteristics of the overall structure by more than 10%.

FIGS. 31A-31D schematically illustrate various embodiments of theframework stacked and rotated. These figures show embodiments where thechords and web members are seamlessly connected so that they become anintegrated unit with structural-member-like features and brace-like webmembers without joints. FIG. 31A shows a first set 2611 of two side byside staggered units 2612 (shown with horizontal stripes). FIG. 31Bshows a second set 2613 of two side by side stagger units 2614. Thesecond unit is a copy of the first unit except rotated by 180° aroundits longitudinal axis and decorated with vertical stripes for thepurpose of illustration. FIG. 31C shows the first set 2611 stackedpartially on top of the second set 2613. This arrangement gives the samefunctionality as a “running bond” with the look of a “stack bond” fronteither side of the wall. FIG. 31D shows how the forward half of thefirst unit (outlined with a bold line) in the foreground looks like itis “stack bonded.”

FIGS. 32A-32J schematically illustrate different embodiments of theframework with curves, bends, twists, bulges, and other distortions.Each figure shows a 5 chord configuration (although each may be formedas a one-piece component rather than by connecting 5 separate chordswith individual web members). FIG. 32A shows an S-shaped framework 2612with a generally uniform thickness along its length. FIG. 32B shows aframework 2614 that is wider in the middle than on the ends. Additionalwidth can be occupied by making cavities of varying width, and/or byusing chords of non-uniform width. FIG. 32C depicts a straight framework2618 with a generally uniform thickness and diagonally extending webmembers 2636. The structure of FIG. 32D is similar to that of FIG. 32Cexcept that the pattern of web members 2638 is different. The framework2622 of FIG. 32E has wider web members 2640 than the web members of FIG.32D. FIGS. 32F, 32G and 32H show frameworks 2624, 2626 and 2628 withnon-uniform thicknesses along their length. The framework 2630 of FIG.321 has curved longitudinal ends 2642, 2644.

FIG. 33 illustrates one embodiment of a framework 2712 in radial formwith web members 2736 and surface web member protrusions 2737. Byremoving one or more of the protrusions, one can create otherembodiments of the disclosed apparatus.

FIG. 34 shows a photo of one embodiment of a three-chord framework,framework 2812, and the most direct metric path 2819 between theoutermost chords of framework 2812.

FIGS. 35A-35C depict embodiments of the framework in a rectangular framewith and without insulating substance in accordance with Example 5. FIG.35A shows an insulative panel 2910 made from five frameworks 2912, 2914,2916, 2918 and 2920. The vertical frameworks 2912 and 2914 andcombination with the horizontal frameworks 2916 and 2918 form a box-typestructure. Vertical framework 2920 acts as a single central stud. Thecross braces 2926, 2928 and 2930 create a stand-off mentioned in theprevious paragraph.

FIG. 36A shows a conventional stud wall 3602 and an insulative stud wall3601 corresponding to an embodiment described herein in accordance withExample 6. The conventional stud wall 3602 has a continuous layer offoam on the exterior with an R-value of 2.5 (° F.·sqft hr/BTU) and anestimated total nominal R-value of 20 (° F.·sqft hr/BTU). Table 3 showsthe values used in the estimate. The estimated total nominal R-value ofthe conventional stud wall 3602 does not include the effects of thermalbridging.

TABLE 3 Nominal normal r_(val) R_(val) Control Stud thickness ° F. sqft/° F. sqft/ Wall 3602 inch (BTUh inch) BTUh stud cavity (true 4 3.7 14.804-inch studs) furring cavity 0 0.00 foam 0.5 5 2.50 siding 0.81sheathing 0.55 drywall 0.5 0.9 0.45 interior air film 0.68 exterior airfilm 0.17 Total 19.96

TABLE 4 normal r_(val) R_(val) Insulative Stud thickness ° F. sqft/ ° F.sqft/ Panel 3601 inch (BTUh inch) BTUh insulative stud 3.5 3.7 12.95cavity furring cavity 1.36 3.7 5.03 foam 0 0.00 siding 0.00 sheathing1.10 drywall 0 0.9 0.00 interior air film 0.68 exterior air film 0.17Total 19.93

TABLE 5 normal r_(val) R_(val) Insulative Stud thickness ° F. sqft/ ° F.sqft/ Panel 359 inch (BTUh inch) BTUh insulative stud 3.5 3.7 12.95cavity furring 0 0.00 foam 0 0.00 siding 0 0.00 sheathing 1.10 drywall 00.00 interior air film 0.68 exterior air film 0.17 Total 14.90

FIG. 36B shows a thermal image of stud walls 3601 and 3602. When theimage was taken, the outdoor temperature was 34° F. and the indoortemperature was 72° F. The low temperature on insulative stud wall panel3601 was 68° F. whereas the low temperature on the conventional studwall 3602 was 57° F.

FIG. 36C shows an embodiment of a rectangular uniaxial framework 359lying down as it might be built while platform framing, for example,with its longitudinal

₃₅₉ direction aligned with the transverse z axis of the figure page.This embodiment of framework 359 has two uniaxially structurallyinsulating stud-like frameworks 370, 370′ and three uniaxiallystructurally insulating cross-brace-like frameworks 361, 361′, 361″.Each of the cross-brace-like frameworks has two webs with two webmembers in a first web, as typified by web member 362, 362′, and one webmember in a second web as typified by web member 364. The web members ineach of web interconnects a pair of structural members as exemplified bythe connection of structural members 361 and 362 by web members 362,362′ and the connection of structural members 362 and 363 by web member364 in cross-brace-like framework 360. Stud-like framework 370′ hasthree structural members 371, 373, and 375. Structural members 371 and373 are connected by web members 372, 372′, 372″ while structuralmembers 373 and 375 are connected by web member 374, 374′, 374″. In anexample, each of the web members is 1.5 inches by 1.5 inches in thelongitudinal y and lateral x directions and 0.7 inches deep in thenormal direction. Each of the structural members is 0.7 inches deep inthe normal direction. The web members within a web are spaced by 13.75inches in all of the stud-like frameworks and all of the brace-likeframeworks. Web members in adjacent webs are offset by 6.125 inchesrelative to each other. Each of stud-like frameworks 370, 370′ is 32inches in longitudinal length, 1.5 inches in lateral width, and 3.5inches in normal depth. Each of cross-brace-like frameworks 360, 360′,360″ is 16.75 inches in longitudinal length, 1.5 inches in lateralwidth, and 3.5 inches in normal depth. Thus, uniaxial framework 359 is19.75 inches (Δ

₃₅₉) by 32 inches (Δ

₃₅₉) by 3.5 inches (Δ

₃₅₉). These key parameters determine that the most direct metric pathbetween the outermost structural members of any framework has a lengthof about 0.7+0.7+6.125+0.7+0.7 inches or 8.925 inches, a span of 3.5inches, a span-wise indirectness of 155%, and a structural insulationfactor of 2.55. The longest direct metric path between the outermoststructural members of any framework has a length of about0.7+0.7+12.25+0.7+0.7 inches or 15.05 inches, a. span of 3.5 inches, aspan-wise indirectness of 330%, and a structural insulation factor of4.3. The average span-wise indirectness is 242% and average structuralinsulation factor is 3.42. The average structural insulation factorsatisfies an average condition for zero thermal bridging which is thatthe average structural insulation factor equal the ratio of theresistivities for the insulating material in the inter-stud-likeframework cavities and the structural material. The insulating materialused in the test was cellulose insulation within a resistivity of 3.7°F.·sqft/(BTUh inch) {25.6 K·m/W}. The structural material was wood witha resisitivity of 1° F.·sqft/(BTUh inch) {6.9 K·m/W}. The averagestructural insulation factor of 3.42 which is within 10% 3.7, i.e. theratio of the resistivities for the insulating material in theinter-stud-like framework cavities and the structural material. Thisembodiment was built as a prototype for thermal testing. Anotherembodiment of this framework has sheets of transparent material similarto the transformation of frame-like framework 780 into window framework780′ illustrated by FIGS. 12E, 12F.

FIG. 36D shows framework 359 with cuboidal pieces of rigid foaminsulation, exemplified by pieces 3661, 3662, 3671, 3761, 3762, 3771,3772, and 3773, inserted into each of the intraframework cavitiesdefined by the structural members and web members. The resistivity ofthe rigid foam insulation was 6.6° F.·sqft/(BTUh·inch) for a totalR-value of 12° F.·sqft/BTUh over the 1.4 cumulative distance of thecavities and including the 2.1 inches of wood with a total R-value of2.1° F.·sqft/BTUh which is also within 10% of the target R-value of 13°F.·sqft/BTUh. In other embodiments pieces of any rigid insulation areused in place of pieces 3661, 3662, 3671, 3761, 3762, 3771, 3772, and3773 both extending beyond the outermost lateral facing surfaces asshown and not extending past the outermost lateral facing surfaces ofthe framework. Pieces of insulation that do extend past the outermostlateral facing surfaces of the framework help to block direct paths ofheat flow along the outermost lateral facing surfaces of the framework.The inter-stud-like-framework cavities between frameworks 370 and 370′and between frameworks 360, 360′, and 360″ were filled with celluloseinsulation enclosed by two pieces of sheathing on opposing sides of theresulting insulated panel.

FIGS. 36F and 36G show the results of thermal imaging. Table 3summarizes the parameters of conventional stud wall 3795 and theparameters of insulative stud-wall module 359. FIG. 36F shows that theconventional stud wall 3602 shows thermal bridging in that the regionsof the wall over the studs 3759 are cold relative to the surroundingportions of wall. The insulative stud wall module 37491 show no thermalbridging in that the regions of the wall over the stud-like frameworksand cross-brace-like frameworks is the same temperature as thesurrounding portions of wall. Conventional stud wall 3602 has a highernominal R-value than the insulative stud wall module 37491. Therefore asecond type of control experiment was performed to compare theinsulative stud wall module 37491 to replica insulative stud wall module38001 which was exactly the same as module except with solid foam forthe webs and no structural web members. FIG. 36G shows that the twomodules perform equally well in that they both have the same eventemperature profile across their interior surfaces. The slightly darkerborder 38002 around the replica insulative stud wall module 38001corresponds to a region where the surrounding insulation was tuckedunder the sheathing at the edge of insulative stud wall module 37491creating a border region of slightly lesser R-value.

FIGS. 36H-36J show the results of testing for a prototype window as oneembodiment. The prototype window has a significantly warmer temperaturethan the standard double pane window. The outdoor temperature was 27° F.on that day. Radiative cooling to the cold sky made surroundingbuildings and surfaces colder than the ambient air temperature. Theprototype picture window 2963 has a frame like the one illustrated inFIG. 12E and five panes of uncoated glass. The energy efficiency isequivalent to that of the surrounding insulation 2966 with an R-value of15.6 (° F.·sqft hr/BTU) as explained in the next few paragraphs. Window2963 keeps the warm side warm, as shown in FIG. 36H, and the cool sidecool, as shown in FIG. 36I. The performance of the window can beimproved by (1) filling the window with an insulative gas and/or (2)applying a low emissivity coating to one or more panes of glass,especially the exterior one. FIG. 36H shows that convective heat flowbetween the window panes makes the top of the window slightly warmerthan the bottom and makes the bottom of the window cooler than the top.The bottom of the window sustains a temperature difference of 75° F.(from 64° F. down to −11° F.) which equals the temperature difference of75° F. (from 66° F. down to −9° F.) sustained by the foam insulation266. Thus, the R-value at the bottom of window 2963 equals that of thefoam insulation 266. The top of window 2963 sustains a temperaturedifference of 77° F. (from 66° F. down to −11° F.) that exceeds thetemperature difference of 75° F. sustained by the surrounding foaminsulation 266. The surrounding insulation (four layers of0.7-inch-thick XPS foamboard) has an R-value per inch of 5.6 (° F.·sqfthr/BTU) per inch, a thickness of 2.8 inches, and a total R-value of 15.6(° F.·sqft hr/BTU) at a mean temperature of 25° F. The actual R-value ishigher because air films between the 4 layers of XPS foamboard increasethe effective R-value per inch of each layer of foam.

FIG. 36I shows that the exterior surface of the window 2970 is colderthan that of the insulation because glass has a higher emissivity (0.92)than insulation (0.6). Therefore a window pane has a relatively highrate of radiative cooling to the sky. FIG. 36J shows that the sky 2983has an extremely cold temperature of −40° F. Notice that the surfaces ofthe building can cool below the ambient air temperature (27° F. on theday the images were acquired) via to the same effect of radiativecooling to the cold sky. This effect is similar to the surfaces of abuilding heating above the ambient air temperature due to radiativeheating by the sun.

FIG. 37 depicts one type of joint used between framework structures,namely a finger joint. Other suitable types of joints are describedbelow.

FIG. 38A-38C illustrate different a non-limiting example of a techniquefor joining frameworks together.

FIG. 38D shows a structure 3210′ that can be made in the general mannerdescribed above in the preceding paragraph with first frameworks 3240′,second frameworks 3242′ and third frameworks 3244′. FIG. 38E shows astructure 3210″ that can be made in the general manner described abovewith first frameworks 3240″, second frameworks 3242″ and thirdframeworks 3244″. FIG. 38F shows a structure 3210′″ that can be made inthe general manner described above with first frameworks 3240′″, secondframeworks 3242′ and third frameworks 3244′.

FIG. 39A shows three embodiments of frameworks 3930, 3940 and 3950 withtwo chords each, exemplified by first chord 3930 and second chord 3932,and with diagonal web members exemplified by diagonal web member 3932 aswell as modifiable, terminal straight-direct web members 3934, 3944,3954. Non-limiting examples of dimensions for chord thickness, chordwidth, web member width, web member angle, etc. are shown.

FIG. 39B shows frameworks 3930, 3940 and 3950 with the modifiable,terminal straight-direct web members 3934, 3944, 3954 modifed intoretaining members 3934′, 3944′, 3954′. Other embodiments of frameworks3930, 3940, 3950 have fewer, possibly zero, removable web members. Otherembodiments of frameworks 3930, 3940, 3950 have more than two removableweb members and do not have retaining members.

FIG. 40 shows a metric path through an apparatus with irregularly shapedpassages, cavities, protrusions, edges, and boundaries of the apparatus(shown with black lines). The line 4107 is an approximation to themetric path from point A to point B created with 10 path segments thatare each straight lines. The approximate length of the metric path frompoint A to point B is the sum of the lengths of all 10 path segments.The range of this metric path is the direct distance between points Aand B. The span must be calculated using the method described in thedefinition of span due to the irregularity of the boundaries. Circle4110 drawn with a dotted line exemplifies one of many circles drawn forthe purposing of determining the line of closest approach between afirst point, point C for this example, on the uppermost boundary of theapparatus and the lowermost boundary on the apparatus. Circle 4110 iscentered on the uppermost boundary and drawn to osculate with thelowermost boundary such that no other circle that osculates with thelowermost boundary has a smaller radius. Circle 4110 is an osculatingcircle of least radius. The dotted line segment 4108 is the line ofclosest approach between the point C on the uppermost boundary and thelowermost boundary. The line of closet approach runs from point C, thecenter of circle 4110 i.e. the osculating circle of least radius, topoint D, i.e. the point where the osculating circle of least radiustouches the lowermost boundary. The line of closest approach serves as adirection line for the purpose of determining the span according to thedefinition. The method illustrated by FIG. 41 is only one of more thanone method for determining the lines of closest approach betweenopposing surfaces of an object. The method of determining the lines ofclosest approach between opposing surfaces for all possible choices ofpoint C on one fo the opposing surfaces, or a representative setthereof, also serves to map out the set of direct paths between opposingsurfaces of an object. The method of determining a line of closestapproach in three dimensions uses an osculating sphere of least radiuscentered at point C and drawing a line from the center of the osculatingsphere of least radius to the point at which the osculating sphere ofleast radius touches the opposing bounday. In general a threedimensional is required unless an object has planar structure that canbe exploited to perform a two dimensional analysis. FIGS. 41A, 41B, 42A,42B <.Provisional Figure #110.> shows different embodiments of anapparatus with a single framework with a uniform shape or I-beam shape.FIG. 41A shows a 93.5″ long, 11″ deep, framework with two 1.5″ wide,2.5″ thick flanges, three 3.5″ wide webs offset by 12″ and 1.25″ thickweb members spaced by 32″ that can serve as joist, stud, rafter, orsimilar building component. FIG. 41B shows a cross section of theframework in FIG. 41A with an I-beam shape created by a 2.5″ wide topflange and bottom flange and 1.5″ wide chords and web members inbetween. FIG. 42A shows the framework in FIG. 41A wherein theweb-members in each different web are offset from web members in allother webs. FIG. 42B shows a cross section of the framework in FIG. 41Awith a 2.5″ wide chords and web-members.

Additional Features

One can combine frameworks in many different ways which basically followthe same pattern as timber framing joinery techniques. One can use scarfjoints, finger joints, finger-scarfing joints, mortise and tenon joints,miter joints, concealed miter joints, dovetail joints, Japanese-typejoints, simple lap joints to name a few. The joint patterns can beapplied in the longitudinal, normal, and lateral directions to lock theframeworks together. Fasteners such as truss plates, mending plates,cables, chain, rope, string, lashing, straps, ties, collars, screws,nails, and dowels can be used to secure frameworks to each other andother structural components. The open architecture of the frameworksallows for rivets, rivnuts, clinched nails, nuts, and bolts to be usedto similar effect and provides an advantage over solid framing membersto use these types of fasteners. One can angle fasteners depending onthe application. One can add features such as actuators, adhesive,apertures, bearings, bushings, buttons, clasps, conduit, cords, cranks,detachable frames, dials, electrical wire, electronic elements, film,flanges, flashing, gaskets, guides, handles, hanging mechanisms,hardware characteristic of doors, hardware characteristic of windows,hinges, holes, hoses, indentations, indicators, insulative mullions,kick plates, knobs, lights, locks, lubricant, metal pieces, mirrors,molding, mullions, o-rings, o-rings, pipes, pockets, protrusions,rabbets, retractable cords, retractors, screens, sealant, seals,sensors, shades, sheathing, solvents, springs, transparent materials,trim, tubing, valves, weather stripping, wheels, and wire. Anotherexample is adding a concave curvature to the outermost chords of a walltruss to flatten the seams between drywall pieces that fall over astud-like framework. Another example is cutting the frameworks intosmaller pieces to produce battens, furring strips, and backer boards forfloating drywall pieces that do not fall over stud-like framework.Another example is applying adhesives, fire-retardants, and othercoatings to frameworks, low-emissivity coatings (particularly windowpanes). Radiant barrier can be applied in the intra-framework,inter-framework cavities, surfaces of a framework. The ideas ofcross-laminated timber, dowel-laminated timber, nail-laminated timber,structural-composite lumber, laminated-veneer lumber, laminated-strandlumber, oriented-strand lumber can be applied to many of the presentembodiments. One can exploit differences in moisture content when usingdowels or floating tenons to make intra-framework and inter-frameworkconnections. One can mill, plane, route, and cut to customize the shapeof manufactured frameworks. One can customize the frameworks on-site bycutting a piece off one framework and fastening it to another. Thereferences cited teach many ideas that can combine with the presentembodiments to produce a wide array of other embodiments. Generally anyvariation described herein for one framework can be applied to any otherframework.

Universal Possibilities

The

,

, and

axes of a framework can have any arbitrary alignment with respect to aset of fixed reference axes x, y, and z. A framework can have anyarbitrary yaw, pitch, or roll and any arbitrary orbital yaw, orbitalpitch, or orbital roll. For instance a structurally insulative stud isan embodiment of an insulative, insulatable framework with its

axis oriented parallel to the vertical y direction defined by gravity.Whereas the same framework oriented with its

axis perpendicular to the vertical y direction defined by gravitybecomes a top plate or bottom plate. Rolling the framework 90°transforms the framework into a joist. Embodiments can be joined withone another. The strongest axis Y of a material that constitutes of aweb member can run parallel to the longitudinal

direction of web member, often enhancing strength, or substantiallynon-parallel or even perpendicular to the longitudinal direction of aweb member, often enhancing insulative resistance. In summary thestrongest axis Y of a material can align in any direction relative tothe longitudinal direction of a web member or any other structural part.Structural members can be flanged. The lateral width of structuralmembers can be greater than that of web members or vice versa. All keygeometric parameters for any given structural part can be customizedrelative to all other structural parts. Key geometric parameters arelateral width, normal depth, longitudinal length, surface qualities,joint structure, shape, twistedness, cuppedness, bowedness, crookedness,kinkiness, smoothness, roundness, squareness, curviness, flateness,planarity, density of wood can be higher in certain places. Physicalparameters such as density can be customized for any given structuralpart. For instance one part could have a higher density or moisturecontent. Higher density material at joints between structural partsrepresents one way of increasing strength of the joint and the overallstructure by extension. The structurally insulative resistance of anymaterial can be enhanced by selectively removing linkages betweenadjacent elongate structural members. A chemical compound can beengineered to selectively bind at specific sites and/or resist bindingat other sites such that a material naturally assembles into anembodiment of the present invention.

The disclosed embodiments can be manufactured with available methods ofmanufacturing and future methods of manufacturing. The disclosedembodiments can be manufactured with currently available materials andmaterials developed in the future. A non-limiting non-exhaustive list ofmaterials includes: metal, ceramics, carbon compounds, carbon nanotubes,graphene, graphite, wood fiber, nanomaterial, nanocrystals, wood,artificial wood, composite materials, wood/plastic composite material,wood-based materials, FRP, fiber-reinforced plastic (FRP), plastic,carbon fiber, kevlar, fiberglass, structural composite, compositeplastic, ceramic, glass, polymer, autoclaved aerated concrete, concrete,stone, brick, compressed earth, mineral, glass, crystalline material,elemental material, colloidal material, transparent material, textile,nanomaterials, biomaterials, composite material, metal, alloy of metals,semiconductor material, structural material, rigid insulation, foam,elements, minerals, chemicals, chemical compounds, insulation

The disclosed embodiments can be engineered and manufactured for allforms of energy. A non-limiting list of methods for manufacturinginsulatable, insulative framework appatuses includes: 3D printing, 3Dprinting with pumped concrete, additive manufacturing, carpentry,carving, casting, chemical deposition, CNC machining, coating, cutting,directed extrusion, dowel lamination, electron beam forming, etching,extrusion, fastening parts with nails, fastening parts with screws,fastening parts together with truss plates, forging, forming, frictionwelding, future industrial process, future manufacturing process,gluing, joinery, joining, lamination with adhesive, lamination, laserablation, laser etching, lashing, machining, masonry, micrwave heatedpressing, milling, molding, nail lamination, permanently clamping andgluing, plasma cutting, plating, pottery, preheated prepressing,pressing, pultrusion, robotic assembly, routing, screw lamination,selective removal of pre-existing material to form a new material withgreater structural insulation factor, self-assembly, sintering,soldering, sputtering, stamping, steam-injection pressing, subtractivemanufacturing, temporarily clamping and gluing, turning, water-jetcutting, weaving, and welding.

Parameters and Ranges

In embodiments, when the apparatus is a building element selected fromthe group consisting of: a stud, joist, rafter, jack, header, windowbuck, door buck, window, door, the minimum rangewise indirectnessbetween the interior face and the exterior face of the building elementis non-zero. The global minimum spanwise indirectness between theinterior face and the exterior face of the building element is greaterthan 0%. This means that the apparatus provides no direct path for theconductive flow of energy between the interior face and exterior face ofthe building. The uniformity of global indirectness between the firstfeature and the second feature has a value of about 0.074 to about0.962, or about 0.222 to about 0.814, or about 0.370 to about 0.666.

In embodiments, when the apparatus is a building element selected fromthe group consisting of: a stud, joist, rafter, jack, header, windowbuck, door buck, window, and door, the minimum rangewise indirectnessbetween the first feature and the second feature is non-zero. The globalminimum path resistance between the first feature and the second featurehas a value of about 3.5 to about 72° F. sqft per BTUh per inch, orabout 4.5 to about 22° F. sqft per BTUh per inch, or about 5.0 to about12° F. sqft per BTUh per inch.

In embodiments, when the building element is a roof truss with a globalminimum spanwise indirectness greater than 0 (0%) between the topsurface of a layer of insulation on the floor of an attic created by theroof truss and the bottom chord of the truss, the maximum and minimumindirectness have values of: about equal to about 200% of being equal,or about 10% to about 150% of being equal, or about 25% to about 100% ofbeing equal, or about 50% to about 75% of being equal.

Methods

Method 1 (designing/building an insulative, insulatable frameworkapparatus)1. Optimize the length of the most direct metric path, i.e., the mostdirect path through the structural material alone excluding thesurrounding space and non-structural material.2. Optimize the cumulative distance between structural membersencountered along the most direct metric path.3. Iterate on 1 and 2 by adjusting the number of structural parts andgeometry of structural parts until achieving satisfactory resultsNote: the identity of the most direct metric path and longest directpath can change during the processwherein the criteria for optimization are:1. strength of the framework apparatus2. least resistance Ra along any path through the framework apparatus,wherein Ra is the lesser of values R1 and R2 as defined in thedefinitions below. <as defined below [1]>.3. optional constraints like: structural strength, cost effectiveness,level of thermal bridging, resistance along the most direct metric path,resistance along the longest direct path, resistance along the shortestdirect path, resistance along the shortest or longest direct path in thesame bundle as the most direct metric path, level of structuralredundancy (for resistance to fire, corrosive chemicals, earthquake,hurricane, wild fire, ballistics, military attack, etc)and adjusting geometry includes but is not limited to:1. modifying the relative position of structural parts2. modifying the dimensions of structural parts3. modifying the cross sectional shape of structural parts (circular,rectangular, trapezoidal, triangular)4. modifying the cross sectional shape of cavities (circular,ellipsoidal, rounded-corner rectangular, rectangular, stadium-shaped,trapezoidal, triangular)Method 2 (designing/building insulated barriers such as frameworks,panels, walls, roofs, floors, etc)Same as method 1 with one additional criterion4. targeted resistance Ro for the whole barrier

Method 3

same as method 2 wherein the targeted resistance Ro is the resistance Rbalong the longest direct path through the non-intervening materialwithin the barrier

Method 4

Method 4 is the same as method 2 wherein the targeted resistance is aminimum required value of Rci

Method 5

To achieve a code-minimum R-value [1] for a two-chord truss, three-chordtruss, or any N-chord truss1.r2=(Rci+Rstd−Rextra)/L2<=>L2=(Rci+Rstd−Rextra)/r2<=>M=sqrt(((Rci+Rstd−Rextra)/r2/S){circumflexover ( )}2−1)<=>Δx=forthcoming formula2. r1=(Rn+Rci−Rextra)/L1<=>L1=(Rn+Rci−Rextra)/r2

Method 6

To practically eliminate thermal bridging for a two-chord truss withdiagonal webs:1. the slope of diagonal web-members in a truss should approximatelyequal r2/rb.2. r1>rb>r2

Method 7

To practically eliminate thermal bridging for a three-chord truss withdiagonal webs:1. the slope of the shortest line segment through a middle chord of athree-chord framework between web-members attached to opposite sides ofthe middle chord should approximately equal r2/rb2. r1>rb>r2

Variations on Methods 1-7

1. Instead of the most direct metric path use the most medial metricpath, i.e., the most medial metric path within the same bundle as themost direct metric path.2. Instead of the most direct metric path use the longest metric path,i.e., the longest metric path within the same bundle as the most directmetric path.3. Instead of the most direct metric path length use the most directmetric path resistance.4. Instead of the most direct metric path length use the most medialmetric path resistance.5. Instead of the most direct metric path length use the longest metricpath resistance.6. Instead of cumulative distance between structural members encounteredalong the most direct metric path use the cumulative thickness ofstructural material crossed by the longest direct path7. Instead of cumulative distance between structural members encounteredalong the most direct metric path use the cumulative web memberthickness for web members encountered along the most direct metric path.7. Instead of cumulative distance between structural members encounteredalong the most direct metric path use the cumulative web memberthickness for web members encountered along the metric path of interest.8. Instead of cumulative distance between structural members encounteredalong the most direct metric path use the longest direct path resistance9. Similar variations changing the metrics.

Definitions Related to Methods 1-7

-   -   Ra: the lesser of values R1 and R2.    -   R1: resistance along the longest direct path through the        structural material of the framework and any intervening        material.    -   R2: resistance along the longest direct path through the        structural material alone.    -   Rb: (in the context of a direct path through a framework        apparatus installed in a barrier) resistance along the longest        direct path through the non-intervening material within the        barrier (barrier-cavity insulation)    -   Rn: 1. R-value of non-continous insulation required by the ICC        building code such as “13” in the “13+5” standard or “20” in the        “20+5” standard [2].    -   Rci: 1. the R-value of continuous insulation required by the ICC        building code such as “+5” in the “13+5” standard or “+10” in        the “13+10” standard [2].    -   Rextra: 1. Rtotal−Ra, 2. the R-value of extra material, outside        the framework, intersected by the longest direct path between        the outer surface and inner surface of a barrier that overlaps        the most direct metric path.    -   Rtotal: 1. R-value along the longest direct path between the        outer surface an inner surface of a barrier that overlaps the        most direct metric path.    -   code-minimum R-value: 1. Rn+Rci where Rn is 13 and Rci is 10 in        the 13+10 standard for example.    -   Rstd: 1. standard R-value associated with the relevant framing        member for a code-minimum R-value such as 3.5° F. sqft/BTUh        associated with a 3.5″ deep wood stud associated with the 13+5        standard [2], 2. rstd multiplied by depth of the relevant        framing member associated with a code-minimum standard such as a        3.5″ deep wood stud associated with the 13+5 standard [2].    -   rstd: 1. standard thermal resistivity value associated with the        relevant framing member for a code-minimum standard such as        1° F. sqft per BTUh per inch associated with a 2×4 wood stud        associated with the 13+5 standard [2].    -   r1: R1 divided by L1    -   r2: R2 divided by L2    -   ra: ra divided by La    -   rb: Rb divided by Lb    -   L1: path length of the longest direct path through the        structural material of the framework and any intervening        material.    -   L2: path length of the most direct metric path    -   La: path length of the path associated with Ra    -   Lb: path length of the longest direct path through the        non-intervening material within the barrier (barrier-cavity        insulation)    -   M: slope of diagonal web-members in a two-chord truss    -   cumulative distance between structural members: 1. (in the        context of a metric path) the sum of distances between each pair        of structural members as measured along the metric path.    -   directness: (in the context of a metric path with a length and a        span) span divided by length    -   direct path: 1. path through the structural material of a        framework and any intervening material with a directness value        of 1.    -   most direct metric path: 1. path through the structural material        of the framework that has the least value of directness, 2. path        through the structural material of the framework that has the        least span-to-length ratio.    -   most direct metric path: 1. most direct path through the        structural material of a framework bypassing any intervening        material, 2. path through the structural material of a framework        bypassing any intervening material with the least value of        directness.    -   most direct path: 1. path through the structural material of the        framework and any intervening material that has the least value        of directness    -   longest direct path: longest direct path through the structural        material of a framework and any intervening material    -   resistance: 1. areal thermal resistance, 2. R-value measured in        Imperial units of ° F. sqft per BTUh and metric units Kelvin by        square meter per Watt, 3. areal resistance associated with any        form of energy transfer    -   resolution: 1. (in the context of a metric path) span of the        metric path divided by the path length of the subpath through        the structural part with the least length measured along the        metric path.    -   path: 1. (in the context of a specified resolution) path as        determined to the specified resolution, 2. (in the context of a        resolution that is not explicitly specified) path as determined        to a resolution of 1000, 3. (in the context of a resolution that        is not explicitly specified but inferrable by context) path as        determined to a resolution inferred by context.    -   span-to-length ratio: (in the context of a path with a span and        a path length) the path length divided by the span.    -   Δx: (in the context of a three-chord truss with web members)        spacing between web-members attached to opposite sides of the        middle chord.

[2]https://codes.iccsafe.org/content/iecc2018/chapter-4-re-residential-energy-efficiency?site_type=public

Method 8 is a method of making and/or using an apparatus with animproved value of minimum spanwise indirectness for at least one metricpath between a first feature and second feature relative to a buildingcomponent of prior art. The method involves reducing thermal bridging byincreasing rangewise indirectness, controlling thermal bridging bycontrolling rangewise indirectness, increasing spanwise indirectness,and/or controlling spanwise indirectness. In embodiments, the methodinvolves increasing spanwise indirectness along metric paths andequalizing the spanwise indirectness along metric subpaths. In somecases, the method comprises controlling spanwise indirectness alongmetric paths and equalizing the spanwise indirectness along metricsubpaths.

Method 9 is a method of manufacturing an apparatus described herein bypultrusion and intermittent insertion and removal of at least onebarrier during the pultrusion process in order to create the cavities.In some cases, the apparatus is manufactured by extrusion andintermittent insertion and removal of at least one barrier during theextrusion process in order to create the cavities.

Method 10 is a method of building a house with crisscrossing furringstrips and the apparatus described herein so as to produce a nonzerospanwise indirectness between the inside and outside of the house.

Method 11 is a method of designing buildings by calculating indirectnessfor the minimized paths and minimized subpaths through the frame of thebuilding;

Method 12 is a method of manufacturing an apparatus described hereinwherein structural members with cooperative finger joints join to formthe whole apparatus. In embodiments, structural members with cooperativefinger joints join to form the whole apparatus wherein the finger jointsare cut with a saw; and/or structural members with cooperative fingerjoints join to form the whole apparatus wherein the finger joints arestamped with a stamping tool with the shape of the negative space of thefinger joints. Strands of lumber are arranged into a mat with the shapeof the apparatus and then pressed into a structural component, and/orveneers of lumber are pressed into a mat with the shape of the apparatusand then pressed into a structural component.

Method 13 is a method of calculating spanwise indirectness for one ormore metric paths through a building frame.

Method 14 is a method of calculating rangewise indirectness for one ormore metric paths through a building frame.

Method 15 is a method of simultaneously maximizing the adiabaticone-dimensional model of effective resistance in combination withmaximizing the spanwise indirectness calculated using the methodsdescribed herein.

Method 16 is a method of simultaneously maximizing the adiabaticone-dimensional model of effective resistance in combination withmaximizing the rangewise indirectness calculated using the methodsdescribed herein.

ADDITIONAL EMBODIMENTS DISCLOSED HEREIN

Embodiment A is an apparatus comprising: a matrix of structure arrays(the structure matrix), a matrix of web arrays (the web matrix), thestructure matrix comprising one or more structure arrays (the structurearrays) and the web matrix comprising one or more web arrays (the webarrays). Each of the web arrays comprises one or more webs (the webs),each of the structure arrays comprising three or more structural members(the structural members), and each of the webs comprising one or moreweb members (the web members). Every two sequential structural membersin every structure array forming a doublet array of first and secondstructural members and an intervening cavity. Every three sequentialstructural members in every structure array forming a triplet array offirst, second, and third structural members. The web matrix isconfigured to give a non-zero rangewise indirectness for the flow ofenergy between the first and third structural members of at least onetriplet array containing only structural members from the firststructure array of the structure matrix. In embodiments, the web matrixis configured to give a non-zero rangewise indirectness for the flow ofenergy between the first and third structural members of at least onetriplet array containing only structural members from the firststructure array of the structure matrix.

Embodiment B is an apparatus comprising: a framework array, a structurematrix, and a web matrix. The framework array comprising one or moreframeworks, and each of the frameworks comprising one or more structurearrays. The structure matrix comprising one or more structure arrays(the structure arrays), the web matrix comprising one or more web arrays(the web arrays), and each of the web arrays comprising one or more webs(the webs). Each of the structure arrays comprises three or morestructural members (the structural members), and each of the webscomprising one or more web members (the web members). Every twosequential structural members in every structure array form a doubletarray and an intervening cavity of first and second structural members,and every three sequential structural members in every structure arrayforming a triplet array of first, second, and third structural members.

In some cases, the web matrix is configured to give a non-zero rangewiseindirectness for the flow of energy between the first and thirdstructural members of at least one triplet array containing onlystructural members from the first structure array of the structurematrix. In embodiments, the web matrix is configured to give a non-zerorangewise indirectness for the flow of energy between the first andthird structural members of at least one triplet array containing astructural member from two different structural arrays. This embodimentincludes a structural member array, the first array, a web array, thesecond array, the cardinality of the first array being three or more,the cardinality of the second array being two or more, each web arraycomprising one or more web members, the first array structural membersbeing spaced apart, every two adjacent structural members in the firstarray forming an adjacent pair, every first-array structural memberadjacent to any adjacent pair forming an adjacent trio, every adjacentpair forming an intervening cavity, with each web contributing anincrease in the rangewise indirectness.

Embodiment C—(See FIGS. 38A, 38B, 38C, 38D, 38E, 38F) Inherently BiaxialFramework Apparatus; Three Structural Members Minimum in at Least 1Framework

Embodiment C is an apparatus comprising an structural parts and a matrixof intraframework cavities, each intraframework cavity defined by a pairof structural parts, the structural parts comprising an array (1) offrameworks, the array of frameworks comprising at least one framework (1a), each framework comprising an array of structural members (2) and anarray of webs (3),—the array of structural members within each frameworkcomprising one or more than one structural member (2 a), and the arrayof structural members within at least one framework comprising three ormore structural members. <.there is a similar embodiment wherein atleast one framework comprises two or more structural members.> Every twoadjacent structural members within every framework forms astructural-member pair (4) of first and second structural members, andevery two adjacent frameworks forms a framework pair (5) of first andsecond frameworks. Every three adjacent structural members within aframework forms a structural-member trio of first, second, and thirdstructural members, and every three adjacent frameworks forms aframework trio of first, second, and third frameworks. Every array ofwebs comprises one intranetworking web (3 a) for each structural-memberpair and one internetworking web (3 b) for each framework pair. Eachintranetworking web for a specified structural-member pair comprises oneor more intranetworking-web members. The intranetworking-web membersconnect the first and second structural members within the specifiedstructural-member pair. Each internetworking web for a specifiedframework pair comprises one or more internetworking-web members, theinternetworking-web members connecting the first and second frameworksof the specified framework pair. The intranetworking webs are configuredto give a minimum rangewise indirectness within a statistical range ofvalues for the flow of energy between the first and third structuralmembers of one or more than one structural-member trio, the statisticalrange of values being selected from the group consisting of: greaterthan zero and 50%, greater than 50% but less than 100%, greater than100% but less than 120%, greater than 120% but less than 140%, greaterthan 140% but less than 160%, greater than 160% but less than 180%,greater than 180% but less than 200%, greater than 200% but less than250%, greater than 250% but less than 300%, greater than 300% but lessthan 400%, greater than 400% but less than 500%, greater than 500%.

In other embodiments the internetworking webs are configured to give aminimum rangewise indirectness within a statistical range of values forthe flow of energy between the first and third frameworks of one or morethan one framework trio, the statistical range of values being selectedfrom the group consisting of: greater than zero and 50%, greater than50% but less than 100%, greater than 100% but less than 120%, greaterthan 120% but less than 140%, greater than 140% but less than 160%,greater than 160% but less than 180%, greater than 180% but less than200%, greater than 200% but less than 250%, greater than 250% but lessthan 300%, greater than 300% but less than 400%, greater than 400% butless than 500%, greater than 500%.

Embodiment D—Sandwich 2D Framework Apparatus—See FIG. 6F

Embodiment D is an apparatus comprising an array (1) of frameworks and amatrix of cavities, the matrix of cavities being formed by the array offrameworks in and of themselves ipso facto, the array of frameworkscomprising one or more than one framework (1 a), each frameworkcomprising an array of structural members (2) and an array of webs (3),the array of structural members within each framework comprising one ormore than one structural member (2 a). The array of structural memberswithin at least one framework comprise three or more structural members,every two adjacent structural members within every framework forming astructural-member pair (4) of first and second structural members, andevery two adjacent frameworks forming a framework pair (5) of first andsecond frameworks. Every three adjacent structural members within aframework form a structural-member trio of first, second, and thirdstructural members, and every three adjacent frameworks form a frameworktrio of first, second, and third frameworks. Every array of webscomprises one intranetworking web (3 a) for each structural-member pair.Each web for a specified structural-member pair comprises one or morenetworking-web members. Each networking-web member connects the firstand second structural members within the specified structural-memberpair, and each networking-web member connects the first and secondframeworks of the specified framework pair. The array of webs isconfigured to give a maximum rangewise indirectness within a statisticalrange of values for the flow of energy between the first and thirdstructural members of one or more than one structural-member trio. Inembodiments, the statistical range of values is as described above inEmbodiment C.

Embodiment E—Lattice 2D Framework Apparatus—See FIG. 17B <.F002.>

Embodiment E is an apparatus comprising an array (1) of frameworks and amatrix of cavities. The matrix of cavities is formed by the array offrameworks in and of themselves ipso facto. The array of frameworkscomprises one or more than one framework (1 a). Each framework comprisesan array of structural formations and an array of webs (3), the array ofstructural formations within each framework comprising one or morestructural formations. The array of structural formations within atleast one framework comprises three or more structural formations, witheach structural formation comprising one or more than one array ofstructural members (2 a). Each array of structural members comprises oneor more than one structural member. Every two adjacent structuralformations within every framework form a structural-formation pair (4)of first and second structural formations, and every two adjacentframeworks forming a framework pair (5) of first and second frameworks.Every three adjacent structural formations within a framework form astructural-member trio of first, second, and third structuralformations, and every three adjacent frameworks forming a framework trioof first, second, and third frameworks. Every array of webs comprisesone intranetworking web (3 a) for each structural-formation pair and oneinternetworking web (3 b) for each framework pair. Each intranetworkingweb for a specified structural-formation pair comprises one or moreintranetworking-web members, with the intranetworking-web membersconnecting all structural members in the first and second structuralformations within the specified structural-formation pair. Eachinternetworking web for a specified framework pair comprises one or moreinternetworking-web members. The internetworking-web members connect thefirst and second frameworks of the specified framework pair. Theintranetworking webs are configured to give a maximum rangewiseindirectness within a statistical range of values for the flow of energythrough one or more than one structural-formation trio between anystructural member in the first structural formation and any structuralmember in the third structural formation. In embodiments, thestatistical range of values is as described above in Embodiment C.

In Embodiments C, D, E and F with three or more frameworks in the arrayof frameworks, the internetworking webs can be configured to give amaximum rangewise indirectness within a statistical range of values forthe flow of energy between the first and third frameworks of one or morethan one framework trio, the statistical range of values being selectedfrom the group consisting of: greater than 0% but less than 1%, greaterthan 1% but less than 10%, greater than 10% but less than 20%, greaterthan 20% but less than 40%, greater than 40% but less than 60%, greaterthan 60% but less than 80%, greater than 80% but less than 100%, greaterthan 100% but less than 120%, greater than 120% but less than 140%,greater than 140% but less than 160%, greater than 160% but less than180%, greater than 180% but less than 200%, greater than 200% but lessthan 250%, greater than 250% but less than 300%, greater than 300% butless than 400%, greater than 400% but less than 500%, greater than 500%.

In Embodiments C, D, E and F with three or more frameworks in the arrayof frameworks, the internetworking webs can be configured to give aminimum rangewise indirectness within a statistical range of values forthe flow of energy between the first and third frameworks of one or morethan one framework trio, the statistical range of values being selectedfrom the group consisting of: greater than 0% but less than 1%, greaterthan 1% but less than 10%, greater than 10% but less than 20%, greaterthan 20% but less than 40%, greater than 40% but less than 60%, greaterthan 60% but less than 80%, greater than 80% but less than 100%, greaterthan 100% but less than 120%, greater than 120% but less than 140%,greater than 140% but less than 160%, greater than 160% but less than180%, greater than 180% but less than 200%, greater than 200% but lessthan 250%, greater than 250% but less than 300%, greater than 300% butless than 400%, greater than 400% but less than 500%, greater than 500%

In Embodiments C, D, E and F with one framework in the array offrameworks, the intranetworking web of the framework being configured togive a maximum rangewise indirectness within a statistical range ofvalues for the flow of energy between the first and third structuralmembers of one or more than one structural-member trio, the statisticalrange of values being selected from the group consisting of: greaterthan 0% but less than 1%, greater than 1% but less than 10%, greaterthan 10% but less than 20%, greater than 20% but less than 40%, greaterthan 40% but less than 60%, greater than 60% but less than 80%, greaterthan 80% but less than 100%, greater than 100% but less than 120%,greater than 120% but less than 140%, greater than 140% but less than160%, greater than 160% but less than 180%, greater than 180% but lessthan 200%, greater than 200% but less than 250%, greater than 250% butless than 300%, greater than 300% but less than 400%, greater than 400%but less than 500%, greater than 500%.

In embodiments C, D, E and F with one framework in the array offrameworks, the intranetworking web of the framework being configured togive a minimum rangewise indirectness within a statistical range ofvalues for the flow of energy between the first and third structuralmembers of one or more than one structural-member trio, the statisticalrange of values being selected from the group consisting of: greaterthan 0% but less than 1%, greater than 1% but less than 10%, greaterthan 10% but less than 20%, greater than 20% but less than 40%, greaterthan 40% but less than 60%, greater than 60% but less than 80%, greaterthan 80% but less than 100%, greater than 100% but less than 120%,greater than 120% but less than 140%, greater than 140% but less than160%, greater than 160% but less than 180%, greater than 180% but lessthan 200%, greater than 200% but less than 250%, greater than 250% butless than 300%, greater than 300% but less than 400%, greater than 400%but less than 500%, greater than 500%.

In embodiments C, D, E and F with one framework in the array offrameworks, the intranetworking web of the framework being configured togive a maximum spanwise indirectness within a statistical range ofvalues for the flow of energy between the first and third structuralmembers of one or more than one structural-member trio, the statisticalrange of values being selected from the group consisting of: greaterthan 0% but less than 1%, greater than 1% but less than 10%, greaterthan 10% but less than 20%, greater than 20% but less than 40%, greaterthan 40% but less than 60%, greater than 60% but less than 80%, greaterthan 80% but less than 100%, greater than 100% but less than 120%,greater than 120% but less than 140%, greater than 140% but less than160%, greater than 160% but less than 180%, greater than 180% but lessthan 200%, greater than 200% but less than 250%, greater than 250% butless than 300%, greater than 300% but less than 400%, greater than 400%but less than 500%, greater than 500%.

In embodiments C, D, E and F with one framework in the array offrameworks, the intranetworking web of the framework being configured togive a minimum spanwise indirectness within a statistical range ofvalues for the flow of energy between the first and third structuralmembers of one or more than one structural-member trio, the statisticalrange of values being selected from the group consisting of: greaterthan 0% but less than 1%, greater than 1% but less than 10%, greaterthan 10% but less than 20%, greater than 20% but less than 40%, greaterthan 40% but less than 60%, greater than 60% but less than 80%, greaterthan 80% but less than 100%, greater than 100% but less than 120%,greater than 120% but less than 140%, greater than 140% but less than160%, greater than 160% but less than 180%, greater than 180% but lessthan 200%, greater than 200% but less than 250%, greater than 250% butless than 300%, greater than 300% but less than 400%, greater than 400%but less than 500%, greater than 500%.

Embodiment F—Two Structural Members Minimum in at Least 1 Framework

Embodiment F is an apparatus comprising an array (1) of frameworks and amatrix of cavities, the matrix of cavities being formed by the array offrameworks in and of itself ipso facto. The array of frameworkscomprises one or more than one framework (1 a), with each frameworkcomprising an array (2) of structural members and an array (3) of webs.The array of structural members within each framework comprises one ormore than one structural member (2 a). The array of structural memberswithin at least one framework comprises two or more structural members.Every two adjacent structural members within every framework forms astructural-member pair (4) of first and second structural members, andevery two adjacent frameworks form a framework pair (5) of first andsecond frameworks. Every three adjacent structural members within aframework form a structural-member trio of first, second, and thirdstructural members, and every three adjacent frameworks forming aframework trio of first, second, and third frameworks. Every array ofwebs comprises one intranetworking web (3 a) for each structural-memberpair and one internetworking web (3 b) for each framework pair, eachintranetworking web for a specified structural-member pair comprisingone or more intranetworking-web members. The intranetworking-web membersconnect the first and second structural members within the specifiedstructural-member pair. Each internetworking web for a specifiedframework pair comprises one or more internetworking-web members. Theinternetworking-web members connect the first and second frameworks ofthe specified framework pair. The intranetworking webs are configured togive a maximum rangewise indirectness within a statistical range ofvalues for the flow of energy between the first and second structuralmembers of one or more than one structural-member pair. In embodiments,the statistical range of values is as described above in Embodiment C.

Embodiment G—Sandwich 2D Framework Apparatus

Embodiment G is an apparatus comprising an array (1) of frameworks and amatrix of cavities, the matrix of cavities being formed by the array offrameworks in and of themselves ipso facto, the array of frameworkscomprising one or more than one framework (1 a), each frameworkcomprising an array of structural members (2) and an array of webs (3),the array of structural members within each framework comprising one ormore than one structural member (2 a). The array of structural memberswithin at least one framework comprise two or more structural members.Every two adjacent structural members within every framework form astructural-member pair (4) of first and second structural members, andevery two adjacent frameworks forming a framework pair (5) of first andsecond frameworks. Every three adjacent structural members within aframework form a structural-member trio of first, second, and thirdstructural members, and every three adjacent frameworks form a frameworktrio of first, second, and third frameworks. Every array of webscomprises one intranetworking web (3 a) for each structural-member pair.Every intranetworking web in the array of webs additionally may be aninternetworking web. Each web for a specified structural-member paircomprises one or more networking-web members. Each networking-web memberconnecting the first and second structural members within the specifiedstructural-member pair. Each networking-web member connects the firstand second frameworks of the specified framework pair. The array of websis configured to give a maximum rangewise indirectness within astatistical range of values for the flow of energy between the first andthird structural members of one or more than one structural-member trio.In embodiments, the statistical range of values is as described above inEmbodiment C.

Embodiment H—Lattice 2D Framework Apparatus

Embodiment H is an apparatus comprising an array (1) of frameworks and amatrix of cavities, the matrix of cavities being formed by the array offrameworks in and of themselves ipso facto, the array of frameworkscomprising one or more than one framework (1 a), each frameworkcomprising an array of structural formations and an array of webs (3),the array of structural formations within each framework comprising oneor more structural formations. The array of structural formations withinat least one framework comprise two or more structural formations. Eachstructural formation comprises one or more than one array of structuralmembers (2 a). Each array of structural members comprises one or morethan one structural member, every two adjacent structural formationswithin every framework form a structural-formation pair (4) of first andsecond structural formations, and every two adjacent frameworks form aframework pair (5) of first and second frameworks. Every three adjacentstructural formations within a framework form a structural-member trioof first, second, and third structural formations, and every threeadjacent frameworks forming a framework trio of first, second, and thirdframeworks. Every array of webs comprises one intranetworking web (3 a)for each structural-formation pair and one internetworking web (3 b) foreach framework pair. Each intranetworking web for a specifiedstructural-formation pair comprises one or more intranetworking-webmembers, the intranetworking-web members connecting all structuralmembers in the first and second structural formations within thespecified structural-formation pair. Each internetworking web for aspecified framework pair comprises one or more internetworking-webmembers, the internetworking-web members connecting the first and secondframeworks of the specified framework pair. The intranetworking webs areconfigured to give a maximum rangewise indirectness within a statisticalrange of values for the flow of energy through one or more than onestructural-formation trio between any structural member in the firststructural formation and any structural member in the third structuralformation. In embodiments, the statistical range of values is asdescribed above in Embodiment C. The indirectness ranges are asdescribed in Embodiment E.

In embodiments, one or more than one framework member is an elementselected from the group consisting of a collection of fibers, acollection of strands, a collection of threads, a collection oflamenelles, and a collection of veneers. In some cases, the framework isa solid formwork with a series of contiguous tunnels.

Embodiment I—Explicitly Uniaxial and Implicitly Multiaxial FrameworkApparatuses

Embodiment I is an apparatus comprising two or more cavities, comprisinga body, and a set of body members, the body exhibiting a set of metricpaths and a first subset of metric paths. The set of body memberscomprises three or more structural members, including first, second, andthird structural members, spaced apart from one another, two or more webmembers, including first and second web members, each connecting atleast one of the three or more structural members to an adjacentstructural member in a fixed positional relationship under self loadingconditions, and together ensuring that every one of the three or morestructural members is connected to the apparatus. The apparatus includestwo or more webs, including a first and second web, each comprising oneor more of the two or more web members, the first web more specificallycomprising the first web member, each web member in the first web atleast connecting the first and second structural members, the second webmore specifically comprising the second web member, each web member inthe second web at least connecting the second and third structuralmembers. Each metric path in the first subset of metric paths is definedby the shortest path along which energy can flow through the bodybetween a first end point, that is, any point on the first structuralmember and a second end point, that is, any point on the thirdstructural member represented by a set of path segments with asufficiently large cardinality. Each metric path is characterized by arange, a path length, and a rangewise indirectness equal to the pathlength divided by the range minus one. The first subset of metric pathsis characterized by a first subset maximum rangewise indirectness equalto the maximum value of the rangewise indirectness for each and everypath therein. The first and second webs are configured to give a firstsubset maximum rangewise indirectness greater than zero. The first andsecond webs are configured to give a value greater than zero for astatistical quantity selected from the group consisting of: maximumvalue of rangewise indirectness, minimum value of rangewiseindirectness, maximum value of spanwise indirectness, and minimum valueof spanwise indirectness.

Embodiment J—Explicitly Uniaxial and Implicitly Multiaxial FrameworkApparatuses

Embodiment J is an apparatus comprising: a body with five or more bodymembers, a first subset of the five or more body members, three or morestructural members each of which is one of the five or more bodymembers, two or more metric paths, a first subset of the two or moremetric paths, two or more pairs of adjacent structural memberscomprising a first paired member of the three or more structural membersand a second paired member of the three or more structural members,adjacent to the first paired member. The apparatus further includes twoor more web members, each of which is one of the five or more bodymembers and connects a pair from the set of two or more pairs ofadjacent structural members together in a fixed positional relationshipunder self loading conditions such that the first paired member does nottouch the second paired member, and two or more webs, each of whichcomprises one or more of the two or more web members. The apparatusexhibits two or more span direction line candidates, a first subset ofthe two or more span direction line candidates, two or more spandirection lines, a first subset of the two or more span direction lines,two or more statistics, and a first subset of the two or morestatistics. The first subset of the five or more body members comprises:a first structural member of the three or more structural members, asecond structural member of the three or more structural members that isoffset away from the interior of the first structural member, a thirdstructural member of the three or more structural members that is offsetaway from the interior of the first structural member to a greaterextent than the second structural member, a first web member of the twoor more web members that connects the first structural member to thesecond structural member, and a second web member of the two or more webmembers that connects the second structural member to the thirdstructural member, a first of the two or more webs, that comprises oneor more of the two or more web members including the first web membereach of which connects the first structural member to the secondstructural member, a second of the two or more webs, that comprises oneor more of the two or more web members including the second web membereach of which connects the second structural member to the thirdstructural member, wherein the set of the two or more metric paths, thefirst subset of the two or more metric paths, the set of the two or morespan direction line candidates, the first subset of the two or more spandirection line candidates, the set of the two or more span directionlines, and the first subset of the two or more span direction lines havea cardinality that is large enough to achieve any required accuracy forthe calculation of any dependent quantities.

Each candidate in the first subset of the two or more span directionline candidates is a line that runs through an initial point, that isany point on the surface of the first structural member and a reflectionpoint, that is the point of closest approach between the initial pointand the third structural member wherein each span direction line in thefirst subset of the two or more span direction lines is a line basedupon a candidate in the first subset of two or more span direction linecandidates and runs through an origination point, that is the point ofclosest approach between the reflection point of the candidate and thefirst structural member and a termination point, that is the point ofcloset approach between the origination point and the third structuralmember.

Each path in the first subset of the two or more metric paths is theshortest path, that is fully confined to the body, between a first endpoint, that is one origination point from the first subset of the two ormore span direction lines, and a second end point, that is onetermination point from the first subset of two or more span directionlines and is approximated by a set of path segments with a cardinalitylarge enough to achieve any required accuracy for the calculation of anydependent quantity. Each path exhibits a range defined as the distancebetween the first end point and the second end point; a path length thatis approximated as the sum total of each segment length for the set ofpath segments; a rangewise indirectness equal to a difference, that isthe path length minus the range, divided by the range, wherein the firstsubset of statistics comprises a first subset maximum rangewiseindirectness equal to the maximum value of each and every rangewiseindirectness for the first subset of the two or more metric paths, suchthat, the first subset maximum rangewise indirectness is greater thanzero.

Embodiment K—Explicitly Uniaxial and Implicitly Multiaxial FrameworkApparatuses, Three Structural Members Minimum, Triplets

Embodiment K is an apparatus comprising: two or more cavities, first,second, and third structural members, spaced apart from one another,first and second webs, each layer comprising one or more structuralmembers, the first and second webs each comprising one or more webmembers, each web member in the first web connecting one or morestructural members in the first layer to one or more structural membersin the second layer, each web member in the second web connecting one ormore structural members in the second layer to one or more structuralmembers in the third layer. Each web member in the first and second websis configured to give a dimensional constraint selected from the groupcomprising: a greater than 0 value of maximum rangewise indirectness, agreater than 0 value of minimum rangewise indirectness, a greater than 0value of maximum spanwise indirectness, and a greater than 0 value ofminimum spanwise indirectness, for the flow of energy along theassociated metric paths between any point at the interface of the firststructural member with the first or more web members, and any point onthe third structural member.

Embodiments L, M N O and P—Uniaxial—Three Structural Members Minimum in1D Framework

Embodiment L is an apparatus comprising: first, second, and thirdstructural members, spaced apart from one another, a first web memberconnecting the first structural member to the second structural member,a second web member connecting the second structural member to the thirdstructural member, the first and second web members being configured togive a maximum rangewise indirectness greater than zero for the flow ofenergy between any point on the first structural member and any point onthe third structural member.

Embodiment M is an apparatus comprising: first, second, and thirdstructural members, spaced apart from one another, a first web member ormore web members connecting the first structural member to the secondstructural member, a second web member or more web members connectingthe second structural member to the third structural member, the firstweb member or more web members and the second web member or more webmembers being configured to give a maximum rangewise indirectnessgreater than zero for the flow of energy between any point on the firststructural member and any point on the third structural member.

Embodiment N is an apparatus comprising first, second, and thirdstructural members, spaced apart from one another, a first web member ormore web members connecting the first structural member to the secondstructural member, a second web member or more web members connectingthe second structural member to the third structural member, the firstweb member or more web members and the second web member or more webmembers being configured to give a minimum rangewise indirectnessgreater than zero for the flow of energy between any point on the firststructural member and any point on the third structural member.

Embodiment O is an apparatus comprising: first, second, and thirdstructural members, spaced apart from one another, a first or more webmembers connecting the first structural member to the second structuralmember, a second or more web members connecting the second structuralmember to the third structural member, the first or more web members andthe second or more web members being configured to give a maximumrangewise indirectness greater than zero for the flow of energy betweenany point at the interface of the first structural member with the firstor more web members, and any point on the third structural member.

Embodiment P is an apparatus comprising three or more structuralmembers, two or more webs, and two or more web members, each of the twoor more webs comprising at least one of the two or more web members andconnecting an adjacent pair of the three or more structural members,that is, a first structural member and an adjacent structural member,exactly one of the two or more webs connecting the first structuralmember to the adjacent structural member of each pair of structuralmembers.

Embodiments Q, R S and T—Explicitly Uniaxial and Implicitly MultiaxialTwo Structural Members Minimum, Doublets

Embodiment Q1 is an apparatus comprising: first and second structuralmembers, spaced apart from one another, a first web member connectingthe first structural member to the second structural member, the firstweb member being configured to give a maximum rangewise indirectnessgreater than zero for the flow of energy between any point at theinterface of the first web member with the first structural member, andany point on the second structural member.

Embodiment Q2 is an apparatus comprising: first and second structuralmembers, spaced apart from one another, a first web member connectingthe first structural member to the second structural member, the firstweb member being configured to give a minimum rangewise indirectnessgreater than zero for the flow of energy between any point at theinterface of the first web member with the first structural member, andany point on the second structural member.

Embodiment R is an apparatus comprising first and second structuralmembers, spaced apart from one another, a first web member connectingthe first structural member to the second structural member, the firstand second web members being configured to give a minimum rangewiseindirectness greater than zero for the flow of energy between any pointon the first structural member and any point on the second structuralmember. In embodiments, the “minimum spanwise indirectness” is greaterthan or equal to 150%±50%, 250%±50%, 350%±50%, 450%±50%, 550%±50%, or650%±50%.

Embodiment S is an apparatus comprising: first and second structuralmembers, spaced apart from one another, a first web member connectingthe first structural member to the second structural member, the firstand second web members being configured to give a normalized spread ofspanwise indirectness that is less than or equal to 50% for the flow ofenergy between any point on the first structural member and any point onthe second structural member.

Embodiment T is an apparatus comprising: first and second structuralmembers, spaced apart from one another, a first web member connectingthe first structural member to the second structural member, the firstand second web members being configured to give a uniformity of spanwiseindirectness less than or equal to 50% for the flow of energy betweenany point on the first structural member and any point on the secondstructural member.

Embodiment U—Triaxial Apparatus—Sandwich Framework

Embodiment U is an apparatus comprising the first apparatus EmbodimentL, and further comprising one special additional layer, one or moreadditional layers, two or more special additional structural members,one or more additional structural members, one or more additional webs,and one or more additional web members wherein the special additionallayer comprises three or more special additional structural members,each of the one or more additional layers comprises one or moreadditional structural members, each of the one or more additional webscomprises one or more of the one or more additional web members, thespecial additional layer has an index of zero, each of the one or moreadditional layers has an index greater than zero, each index is aninteger between zero and the number of the one or more additionallayers, each index greater than one forms a pair of adjacent indicescomprising a first index and second index that equals the first indexminus one, and each pair of adjacent indices forms a pair of adjacentlayers between a first layer, the one of the one or more additionallayers with an index equal to the first index in the pair of adjacentindices, and a second layer, the one of the one or more additionallayers with an index equal to the second index in the pair of adjacentindices. As a result, each of the two or more webs in the first set ofthe first apparatus connects to two of the one or more specialadditional structural members, each one of the one or more additionalwebs connects each of the one or more additional layers to the thirdapparatus, and each of the one or more additional web members connectstwo of the additional structural members in the first layer in a pair ofadjacent layers to the second layer in the pair of adjacent layers.

Embodiment V1—Single Solid Body Apparatus

Embodiment V1 is an apparatus in which the material of the apparatusfills each and every seam at the interface between the apparatus memberswherein the apparatus members are the structural members and web membersto form a solid body with structural-member-like parts and aweb-member-like parts.

Embodiment V2 is an apparatus in which the material of the apparatusfills one or more seams, up to a maximum of one fewer than all seams, atthe interface between the apparatus members wherein the apparatusmembers are the structural members and web members.

Embodiment W—Single Solid Body

Embodiment W is a window frame formed by adding a through-going cavityto the framework described in Embodiment L in the spanwise direction. Inembodiments, one or more of the apparatus members has a different lengththan the others wherein the apparatus members are the structural membersand web members.

Embodiment X is a framework as described above that is incorporated intoa window opening, door opening, penetration, circular opening, portal,insulation cavity, room, chamber, indentation, open cavity, closedcavity, closed cell, capsule, microscopic cavity, nanoscopic cavity, andinsignificant cavity.

Embodiment Y is similar to Embodiment L and further includes one specialadditional layer, one or more additional layers, two or more specialadditional structural members, one or more additional structuralmembers, one or more additional webs, and one or more additional webmembers, wherein the special additional layer comprises three or morespecial additional structural members, each of the one or moreadditional layers comprises one or more additional structural members,each of the one or more additional webs comprises one or more of the oneor more additional web members. In embodiments, the special additionallayer has an index of zero, each of the one or more additional layershas an index greater than zero, each index is an integer between zeroand the number of the one or more additional layers, each index greaterthan one forms a pair of adjacent indices comprising a first index andsecond index that equals the first index minus one, and each pair ofadjacent indices forms a pair of adjacent layers between a first layer,the one of the one or more additional layers with an index equal to thefirst index in the pair of adjacent indices, and a second layer, the oneof the one or more additional layers with an index equal to the secondindex in the pair of adjacent indices

As a result, each of the two or more webs in the first set of the firstapparatus connects to two of the one or more special additionalstructural members, each one of the one or more additional webs connectseach of the one or more additional layers to the third apparatus, andeach of the one or more additional web members connects two of theadditional structural members in the first layer in a pair of adjacentlayers to the second layer in the pair of adjacent layers. In thisembodiment, the first feature is the most distal structural member alonga first axis, the second feature is the most proximal structural memberalong the first axis, the third feature is the most distal structuralmember along a second axis, the fourth feature is the most proximalstructural member along the second axis, and the second axis runs at anangle with respect to the first axis

Embodiment Z

Embodiment Z is a temporary formwork that contains permanently installedautoclaved aerated concrete blocks arranged in a pattern of cavities forforming a concrete framework by pouring concrete into said formwork suchthat the concrete framework has a minimum spanwise indirectness of 0.25(25%) for at least one minimized path between faces of the concreteframework that oppose one another in the depthwise direction

Embodiment AB is a window framework as described above that includes avalve for depressurizing the space between at least two window paneswhen the valve is open and for resealing the space so as to preserve thelow pressure within when the valve is closed. A household vacuumcleaner, handheld pump, or other suction device can depressurize thespace with an appropriate fitting to mate with that of the window valveport. In some cases, this embodiment comprises a framework includingthree layers of offset encapsulated cells. In some cases, the frameworkpieces are formed from three struts connected by two webs.

Embodiment AC is an apparatus as described in the last paragraph of theSummary and in claims 16 and 17, further comprising any number ofadditional structural-members for a total of N_sm structural-memberslabeled by a structural-member-array, any number of additional webs fora total of N_w webs labeled by a web-array,

-   -   the first web further comprising any number of additional        web-members for a total of N_wm web-members in the first web,    -   the second web further comprising any number of additional        web-members for a total of N_wm web-members in the second web,    -   the structural-member-array indexed by an index, I_sm, that        ranges between 1 and N_sm,    -   the first structural-member indexed by I_sm equal to 1,    -   the second structural-member indexed by I_sm equal to 2,    -   the third structural-member indexed by I_sm equal to 3,    -   the I_sm^(th) structural-member positioned between the        (I_sm−1)^(th) and (I_sm+1)^(th) for I_sm running from 2 to        N_sm−1,    -   the web-array indexed by an index, I_w, that ranges between 1        and N_sm−1,    -   the first web indexed by I_w equal to 1,    -   the second web indexed by I_w equal to 2,    -   the I_w^(th) web comprising a number of web-members,        I_w^(th)-web N_wm, ranging between 1 and any positive integer        greater than zero,    -   the I_w^(th) web indexed by an index, I_w^(th)-web I_wm, that        ranges between 1 and I_w^(th)-web N_wm,    -   the first web comprising the first web-member,    -   the second web comprising the second web-member,    -   the first web-member indexed by a first-web N_wm value of 1,    -   the second web-member indexed by a second-web N_wm value of 1,    -   each web-member in the I_w^(th) web connecting the I_w^(th)        structural-member to the (I_w+1)^(th) structural-member in a        spaced apart relationship for I_w running from 1 to the I_w^(th)        N_wm,    -   the structural parts further comprising the additional        structural-members and additional webs and constituting a        uniaxial framework,

Embodiment AD is the combination of embodiment AB with at least oneadditional framework for a total of N_f frameworks, and N_f−1internetworking-web-arrays,

-   -   the frameworks labeled by a framework-array,    -   the framework-array indexed by an index, I_f,    -   the index, I_f, ranging between 1 and N_f,    -   the internetworking-web-arrays labeled by a        internetworking-web-array-matrix,    -   the internetworking-web-array-matrix comprising a number, N_iwa,        of internetworking-web-arrays,    -   the number, N_iwa, being at least one,    -   the internetworking-web-array-matrix indexed with an index,        I_iwa, that specifies the internetworking-web-array,    -   I_iwa, running between 1 and N_f−1,    -   the I_iwa^(th) internetworking-web-array comprising a number, an        I_iwa^(th) N_iw, of internetworking webs,    -   the I_iwa^(th) N_iw, being at least one,    -   the I_iwa^(th) internetworking-web-array indexed by an index,        the I_iwa^(th) I_iw, that specifies the I_iwa^(th) I_iw^(th)        internetworking-web-array,    -   the I_iwa^(th) I_iw running between 1 and I_iwa^(th) N_iw,    -   the I_iwa^(th) I_iw^(th) internetworking-web comprising a        number, the I_iwa^(th) I_iw^(th) N_iwm, of        internetworking-web-members,    -   the I_iwa^(th) I_iw^(th) N_iwm being at least one,    -   the I_iwa^(th) I_iw^(th) internetworking-web indexed by an        index, the I_iwa^(th) I_iw^(th) I_iwm, that specifies the        I_iwa^(th) I_iw^(th) I_iwm^(th) internetworking-web-member,    -   the I_iwa^(th) I_iw^(th) I_iwm running between 1 and I_iwa^(th)        I_iw^(th) iN_iwm,    -   the I_iwa^(th) I_iw^(th) internetworking-web connecting the        I_iwa^(th) framework to the (I_iwa+1)^(th) framework for I_iwa        running from 1 to N_f−1,    -   the I_iwa^(th) I_iw^(th) internetworking-web comprising at least        one internetworking-web-member that connects at least one        structural-member in the I_iwa^(th) framework to at least one        structural-member in the (I_iwa+1)^(th) framework,    -   the structural parts further comprising the        internetworking-web-arrays and additional frameworks,    -   the structural parts constituting a multiaxial framework,

Embodiment AE is Embodiment AC wherein wherein the structural parts aredimensioned and positioned so as to comprise at least one of (A) a mostdirect second path through the uniaxial frameworks starting from thefirst structural-member at least 1.5 times longer than the span of themost direct second path through the uniaxial frameworks starting fromthe first structural-member or (B) a most direct second path through theuniaxial frameworks starting from the first structural-member at least 2times longer than the span of the most direct second path through theuniaxial frameworks starting from the first structural-member or (C) amost direct second path through the uniaxial frameworks starting fromthe first structural-member at least 2.5 times longer than the span ofthe most direct second path through the uniaxial frameworks startingfrom the first structural-member or (D) a most direct second paththrough the uniaxial frameworks starting from the firststructural-member at least 3 times longer than the span of the mostdirect second path through the uniaxial frameworks starting from thefirst structural-member. In some cases each internetworking web-memberis a piece of rigid insulation.

Embodiment AF is an apparatus comprising at least one of an array ofstructural formations, each structural formation comprising an array ofstructural members, each structural member comprising an array ofstructural sub-members and an array of webs, each web comprising anarray of web members, each web comprising at least one of: (a) aninterformation web, wherein the interformation web members areconfigured to give a span-wise indirectness greater than 100% for theshortest metric path between first and last formations within an arrayof structural formations.

Embodiment AF: (Preferred Embodiment) for installation in a barrier witha cooperative interior surface and exterior surface, an apparatuscomprising a framework with more than one structural member and a globalweb comprising more than zero global web members wherein the global webmembers are configured to give (1) a first metric path between theinterior surface and exterior surface with a first length L₁ a firstspan S₁ a first span-wise indirectness I₁={L₁/S₁}−1 greater than 100%(insulative aspect) equivalent to a first structural insulation factorF₁=L₁/S₁ greater than 2 wherein the first metric path is shorter thanany other metric path between the interior and exterior surfaces, (2) afirst direct path between the interior and exterior surfaces with asecond span and a first cumulative distance between structural parts (a)greater than {(9%±1%) times the second span} (insulatable aspect) and(b) less than {80% times the second span} (not so insulatable that thestructure becomes weak) wherein the first cumulative distance betweenstructural parts is less than any other cumulative distance betweenstructural parts for any other direct path between the interior andexterior surfaces, (3) a first path length that is less than 85 timesfirst cumulative distance between structural parts (balance between theinsulatable and insulative aspects).

wherein the structural parts include each structural member and theglobal web.

Embodiment AG: Embodiment AF wherein the same rules apply in directionperpendicular to the structural members.

In another embodiment of the present invention, a panel structure 500shown in FIG. 43 includes spaced first planar panel 502, second planarpanel 504 and a plurality of spaced structural members 510A, 510B, 510C,510D connecting facing surfaces of the first panel 502 and second panel504. As shown in FIG. 44, each of the structural members 510A, 510B,510C, 510D includes a first frame member 520 in contact with the firstplanar panel 502 in a longitudinal direction, a second frame member 530in contact with the second planar panel 504 in the longitudinaldirection, the second frame member 530 being spaced from andsubstantially parallel to the first frame member 520, and a connectingframe member 540 between and contacting the first frame member 520 andsecond frame member 530, the connecting frame member 540 contacting thefirst frame member 520 at a plurality of first locations 525 andcontacting the second frame member 530 at a plurality of secondlocations 550, the first and second frame members 520, 530 having freeinterior-facing surfaces 521, 531 between the first and second locations525, 550. The connecting frame member 540 provides no direct path ofconductive heat flow, in a direction perpendicular to the longitudinaldirection, between interior-facing surfaces 521, 531 of the first andsecond frame members 520, 530. The structural members 510A, 510B, 510C,510D may be made of wood or a composite thereof. The distance betweenfirst locations 525 is at least 2 times the distance between the firstand second frame members 520, 530. The distance between second locations550 is at least 2 times the distance between the first and second framemembers 520, 530. The connecting frame member 540 comprises a centralframe member 540A substantially parallel to the first and second framemembers 520, 530 and a plurality of linking members 540B, 540Cperpendicular to the central frame members 540A in contact with thefirst and second frame members 520, 540 at the first and secondlocations 525, 550. Alternately the connecting frame member 540comprises a central frame member 540A substantially parallel to thefirst and second frame members 520, 540 and a plurality of first linkingmembers 540B connecting a first surface 550 of the central frame member540A to the first frame member 530 and a plurality of second linkingmembers 540C connecting a second surface of the central frame member540A opposite the first surface of the central frame member 540A to thesecond frame member 520, wherein none of the first linking members 540Bare directly opposite any of the second linking members 540C. As shownin FIG. 44, the connecting frame member 540 comprises a central framemember 540A substantially parallel to the first and second frame members520, 530 and a plurality of linking members 540B, 540C, each linkingmember 540B, 540C secured either diagonally between the first framemember 530 and the central frame member 540A or diagonally between thesecond frame member 520 and the central frame member 540A. The panelstructure 500 may include secondary linking members connecting one ofthe spaced structural members to at least one other spaced structuralmember. The secondary linking members may connect one of the spacedstructural members to at least one other spaced structural memberwherein the secondary linking members provide no direct path ofconductive heat flow, in a direction perpendicular to the longitudinaldirection, between spaced structural members.

Another aspect of the present invention is directed to a method ofmaking a panel structure 500, shown in FIG. 45, the facing surfaces ofthe first and second panels are connected using the structural members510A, 510B, 510C, 510D wherein the connecting frame member 540 providesno direct path of conductive heat flow in a direction perpendicular tothe longitudinal direction, between interior-facing surfaces of thefirst and second frame members 520, 530.

Alternately, the method of making a panel structure 500 may include theplurality of spaced structural members 510A, 510B, 510C, 510D connectingthe facing surfaces of the first and second panels 502, 504 wherein thespaced structural members 510A, 5108, 510C, 510D provide no direct pathof conductive heat flow in a direction perpendicular to the longitudinaldirection, between interior-facing surfaces of the first and secondpanels 502, 504.

Another aspect of the present invention is directed to a structuralmember 510A, 510B, 510C, 510D which connects a first and a second panel502, 504 to make a panel structure 500. The structural member 510A,510B, 510C, 510D includes a first elongated frame member 520, a secondelongated frame member 530 spaced from and substantially parallel to thefirst elongated frame member 520 and a connecting frame member 540between and contacting the first and second frame members 520, 530, theconnecting frame member 540 contacting the first frame member 530 at aplurality of first locations 550 and contacting the second frame member520 at a plurality of second locations 525, the first and second framemembers 520, 530 having free interior-facing surfaces between the firstand second locations 550, 525. The connecting frame member 540 providesno direct path of conductive heat flow, in a direction perpendicular tothe longitudinal direction, between interior-facing surfaces of thefirst and second frame members 520, 530.

Another aspect of the present invention shown in FIG. 46 is directed toan insulative structural member 610 including a first elongated framemember 620 having a first length and a second elongated frame member 630spaced from and substantially parallel to the first elongated framemember 620, the second elongated frame member 630 having a second lengthsubstantially the same as the first length. The insulative structuralmember 610 includes a central elongated frame member 640 spaced betweenand parallel to the first and second frame members 620, 630, the centralframe member 640 having a third length substantially the same as thefirst length. The insulative structural member 610 includes a pluralityof first connecting members 650 joining the first elongated member 620to one surface of the central frame member 640, the first connectingmembers 650 having a connection length shorter than the first length.The insulative structural member 610 includes a plurality of secondconnecting members 660 joining the second elongated member 630 to anopposite surface of the central frame member 640, the second connectingmembers 660 having a connection length substantially shorter than thefirst length.

The structural member 610 provides no direct path of conductive heatflow, in a direction perpendicular to the first length. The connectionlength of the plurality of first connecting members 650 and theplurality of second connecting members 660 may be less than 20% of thefirst length of the first elongated frame member 620 and additionallymay be less than 10% of the first length of the first elongated framemember. The first, second and central elongated members 620, 630, 640each may comprise a plurality of elongated lamination members 601 asshown in FIG. 46 and the first and second connecting members 650, 660comprise a plurality of connecting lamination members 602. Theconnecting lamination members of the first connecting members 650 may beinterwoven with the elongated lamination members of the first andcentral elongated members 620, 640 and the connecting lamination membersof the second connecting members 660 may be interwoven with theelongated lamination members of the second and central elongated members630, 640. The first and second connecting members 650, 660 may besecured diagonally between the corresponding first or second elongatedframe member 620, 630 and the central frame member 640. The first andsecond connecting members may be configured to give a first metric pathbetween an outside surface of the first elongated frame member anopposing outside surface of the second elongated frame member with afirst length L1 a first span S1 a first span-wise indirectnessI1={L1/S1}−1 greater than 100% (insulative aspect) equivalent to a firstgeometrical insulation factor F1=L1/S1 greater than 2, wherein the firstmetric path is shorter than any other metric path between the interiorand exterior surfaces. The first and second connecting members may beconfigured to give a first direct path between an outside surface of thefirst elongated frame member an opposing outside surface of the secondelongated frame member with a second span and a first cumulativedistance between structural parts (a) greater than {(9%±1%) times thesecond span} (insulatable aspect) and (b) less than {80% times thesecond span} (not so insulatable that the structure becomes weak)wherein the first cumulative distance between structural parts is lessthan any other cumulative distance between structural parts for anyother direct path between the interior and exterior surfaces. The firstand second connecting members may be configured to give a first pathlength that is less than 85 times first cumulative distance betweenstructural parts (balance between the insulatable and insulativeaspects). wherein the structural parts include each structural memberand the first and second connecting member.

Thus, the present invention provides one or more of the followingadvantages. The present invention provides a structural member which hasinsulative properties and provides a structural member which complimentinsulative materials used with the structural member. The presentinvention provides a structural member for supporting panels on opposingsides of the structural member which resists heat transfer between theopposing panels and provides a panel structure having spaced first andsecond planar panels which provide structural integrity and resistanceto heat transfer.

While the present invention has been particularly described, inconjunction with one or more specific embodiments, it is evident thatmany alternatives, modifications and variations will be apparent tothose skilled in the art in light of the foregoing description. It istherefore contemplated that the appended claims will embrace any suchalternatives, modifications and variations as falling within the truescope and spirit of the present invention.

1-32. (canceled)
 33. An insulative structural member comprising: a firstelongated frame member having a first length; a second elongated framemember spaced from and substantially parallel to the first elongatedframe member, the second elongated frame member having a second lengthsubstantially the same as the first length; a central elongated framemember spaced between and parallel to the first and second framemembers, the central frame member having a third length substantiallythe same as the first length; a plurality of first connecting membersjoining the first elongated frame member to the central frame member,the first connecting members having a connection length shorter than thefirst length; and a plurality of second connecting members joining thesecond elongated frame member to the central frame member, the secondconnecting members having a connection length substantially shorter thanthe first length; providing: a first direct path between exterior-facingsurfaces of the first and second frame members with a first-direct-pathspan and a maximum cumulative distance between structural parts that isgreater than any other cumulative distance between structural parts forany direct path between exterior-facing surfaces of the first and secondframe members; a first most-direct metric path between the firstelongated frame member and second elongated frame member with a firstpath length L1, a first span S1, and a first span-wise indirectnessI1={L1/S1}−1 that is less than any other span-wise indirectness for anyother most-direct metric path between the first and second framemembers; a second most-direct metric path between the first elongatedframe member and second elongated frame member with a second path lengthL2, a second span S2, and a second span-wise indirectness I2={L2/S2}−1that is less than any other span-wise indirectness for any othermost-direct metric path between the first and second frame members inthe same bundle of metric paths but is greater than any other minimumvalue of span-wise indirectness for any other bundle of metric paths;and being configured as one of a; first-type insulative structuralmember, second-type insulative structural member, third-type insulativestructural member, fourth-type insulative structural member, fifth-typeinsulative structural member, sixth-type insulative structural member,seventh-type insulative structural member, eighth-type insulativestructural member, ninth-type insulative structural member, tenth-typeinsulative structural member, eleventh-type insulative structuralmember, twelfth-type insulative structural member, thirteenth-typeinsulative structural member, fourteenth-type insulative structuralmember, and fifteenth-type insulative structural member; wherein thefirst-type insulative structural member is configured to provide nodirect path of conductive heat flow through the structural parts, in adirection perpendicular to the longitudinal direction, betweeninterior-facing surfaces of the first and second frame members;second-type insulative structural member is configured to make the firstspan-wise indirectness I1 between 0% and 10% (insulative aspec);third-type insulative structural member is configured to make the firstspan-wise indirectness I1 between 10% and 25% (insulative aspec);fourth-type insulative structural member is configured to make the firstspan-wise indirectness I1 between 25% and 50% (insulative aspec);fifth-type insulative structural member is configured to make the firstspan-wise indirectness I1 between 50% and 75% (insulative aspec);sixth-type insulative structural member is configured to make the firstspan-wise indirectness I1 between 75% and 100% (insulative aspec);seventh-type insulative structural member is configured to make thefirst span-wise indirectness I1 greater than 100% (insulative aspec);eighth-type insulative structural member is configured to make thesecond span-wise indirectness I2 between 0% and 10% (insulative aspec);ninth-type insulative structural member is configured to make the secondspan-wise indirectness I2 between 10% and 25% (insulative aspec);tenth-type insulative structural member is configured to make the secondspan-wise indirectness I2 between 25% and 50% (insulative aspec);eleventh-type insulative structural member is configured to make thesecond span-wise indirectness I2 between 50% and 75% (insulative aspec);twelfth-type insulative structural member is configured to make thesecond span-wise indirectness I2 between 75% and 100% (insulativeaspec); thirteenth-type insulative structural member is configured tomake the second span-wise indirectness I2 greater than 100% (insulativeaspec); fourteenth-type insulative structural member is configured togive a maximum cumulative distance between structural parts greater than{(9%±1%) times the first-direct-path span} and less than {80% times thefirst-direct-path span} (insulatable aspect but not so insulatable thatthe structure becomes weak); fifteenth-type insulative structural memberis configured to give a maximum cumulative distance between structuralparts greater than {(9%±1%) times the first-direct-path span} and lessthan {60% times the first-direct-path span} (insulatable aspect but notso insulatable that the structure becomes weak); sixteenth-typeinsulative structural member is configured to give a maximum cumulativedistance between structural parts greater than {(9%±1%) times thefirst-direct-path span} and less than {50% times the first-direct-pathspan} (insulatable aspect but not so insulatable that the structurebecomes weak); and the structural parts include the elongated framemembers, plurality of first connecting members, and plurality of secondconnecting members.
 34. The insulative structural member of claim 33further comprising: any number of additional frame members; any numberof additional connecting members that each connect at least two members;any number of additional frame members as part of the central framemember; any number of additional connecting members as part of thecentral frame member that each connect at least two members; any numberof protrusions that each have at least one point of connection to atleast one other member, and any amount of insulative material betweenany number of frame members; a foil radiant barrier attached to anysurface; wherein: additional members include additional frame members,and additional connecting members; members include first connectingmembers, second connecting members, frame members, protrusions, andadditional members; connecting members include first connecting members,second connecting members, and protrusions; any number of the membersare straight; any number of the members are curved; any pair of themembers are aligned; any pair of the members are parallel; any number ofthe members protrude in any direction perpendicular to any of the framemembers; any number of the members protrude in a direction parallel toany of the frame members; any number of the members comprise a pluralityof elongated lamination members secured to adjacent elongated laminationmembers; any number of members are made from a non-metallic material;any number of members are made from a wood-based material; anyconnecting member is any portion of a woodworking joint; any connectingmember incorporates any portion of a woodworking joint; any frame memberincorporates any portion of a woodworking joint; any frame member is anyportion of a woodworking joint; any number of connecting members areoffset from nearest neighboring connecting members along the length of aconnected frame member; any number of connecting members have asubstantially similar thickness to at least one of the frame members towhich the connecting member connects; any number of the connectingmembers run diagonally relative to a connected frame member; any numberof the connecting members run parallel relative to a connected framemember; any number of the connecting members run perpendicular relativeto a connected frame member; any number of the additional connectingmembers run diagonally relative to a connected frame member; any numberof the additional connecting members run parallel relative to aconnected frame member; and any number of the additional connectingmembers run perpendicular relative to a connected frame member.
 35. Theinsulative structural member of claim 34 wherein: the connection lengthof the plurality of first connecting members and the plurality of secondconnecting members is less than 20% of the first length of the firstelongated frame member.
 36. The insulative structural member of claim 34wherein: the first, second and central elongated members each comprise aplurality of elongated lamination members secured to adjacent elongatedlamination members, and the first and second connecting members comprisea plurality of connecting lamination members secured to adjacentconnecting lamination members.
 37. The insulative structural member ofclaim 36 wherein: the connecting lamination members of the firstconnecting members are interwoven with the elongated lamination membersof the first and central elongated members and the connecting laminationmembers of the second connecting members are interwoven with theelongated lamination members of the second and central elongatedmembers.
 38. The insulative structural member of claim 34 wherein: anyof the first and second connecting members are secured diagonallybetween the corresponding first or second elongated frame member and thecentral frame member.
 39. The insulative structural member of claim 34being configured to make: the second span-wise indirectness I2 greaterthan 5% (insulative aspect).
 40. The insulative structural member ofclaim 34 wherein the first and second connecting members are configuredto make the second path length L2 less than 40 times the maximumcumulative distance between structural parts (balance between theinsulatable and insulative aspects).
 41. The insulative structuralmember of claim 34 being configured to make: the first span-wiseindirectness I1={L1/S1}−1 greater than 5% (insulative aspect); themaximum cumulative distance between structural parts greater than 15%and less than {(60%±5%) times the first-direct-path span} (insulatableaspect but not so insulatable that the structure becomes weak); and thefirst path length L1 less than 20 times the maximum cumulative distancebetween structural parts (balance between the insulatable and insulativeaspects).
 42. A frame apparatus comprising at least one insulativestructural member of claim 34, the frame apparatus configured as one ofa: rafter, purlin, header, joist, floor joist, joist hanger, rim joist,bottom plate, crown plate, double bottom plate, double top plate, plate,sill plate, sole plate, top plate, beam, I-beam, L-Beam, T-beam, Z-Beam,column, girder, post, cripple stud, jack stud, king stud, stud, wallstud, girt, Z-girt, floor truss, floor-truss chord, roof truss,roof-truss chord, truss, truss chord, truss web, rib, buck, casement,casing, jamb, mullion, muntin, rail, stile, sill, transom, and framingcomponent; insulated rafter, insulated purlin, insulated header,insulated joist, insulated floor joist, insulated joist hanger,insulated rim joist, insulated bottom plate, insulated crown plate,insulated double bottom plate, insulated double top plate, insulatedplate, insulated sill plate, insulated sole plate, insulated top plate,insulated beam, insulated I-beam, insulated L-beam, insulated T-beam,insulated Z-beam, insulated column, insulated girder, insulated post,insulated cripple stud, insulated jack stud, insulated king stud,insulated stud, insulated wall stud, insulated girt, insulated Z-girt,insulated floor truss, insulated floor-truss chord, insulated rooftruss, insulated roof-truss chord, insulated truss, insulated trusschord, insulated truss web, insulated rib, insulated buck, insulatedcasement, insulated casing, insulated jamb, insulated mullion, insulatedmuntin, insulated rail, insulated stile, insulated sill, insulatedtransom, insulated framing component; insulative curved containerwherein the frame members form continuous curved nested surfaces thatwrap around an inner space; insulative container wherein the framemembers form continuous nested surfaces that wrap around an inner space;cross-laminated panel wherein each frame member comprises a laterallyextending array of planks joined together edge-to-edge and eachconnecting member joins adjacent arrays of planks as well as plankswithin each array of planks; insulated cross-laminated panel whereineach frame member comprises a laterally extending array of planks joinedtogether edge-to-edge, each connecting member joins adjacent arrays ofplanks as well as planks within each array of planks, and insulationfills the space between adjacent connecting members and adjacent framemembers; dowel-laminated panel wherein each frame member comprises alaterally extending array of planks joined together edge-to-edge andeach connecting member is a dowel that joins planks in adjacent array ofplanks; insulated dowel-laminated panel wherein each frame membercomprises a laterally extending array of planks joined togetheredge-to-edge, each connecting member is a dowel that joins planks inadjacent array of planks, and insulation fills the space betweenadjacent connecting members and adjacent frame members; dowel-laminatedplank framework wherein each frame member is a plank and each connectingmember is a dowel; insulated dowel-laminated plank framework whereineach frame member is a plank, each connecting member is a dowel, andinsulation fills the space between adjacent connecting members andadjacent frame members; insulative biaxial framework comprising aplurality insulative structural members including the at least oneinsulative structural member and further comprising additionalconnecting members that connect at least two insulative structuralmembers wherein the additional connecting members provide no direct pathfor conductive heat flow between a first frame member of an outermostinsulative structural member and a first frame member of an opposingoutermost insulative structural member; biaxial framework comprising aplurality insulative structural members including the at least oneinsulative structural member and further comprising additionalconnecting members that connect at least two insulative structuralmembers wherein the maximum cumulative distance between structuralmembers is less than 80% of the distance between a pair of outermostinsulative structural members; tubular biaxial framework comprising aplurality of insulative structural members further comprising additionalconnecting members that connect at least two adjacent structural memberswherein the frame members are concentric rings, each with an N-sidepolygonal shape; tubular framework comprising a plurality insulativestructural members, including the at least one insulative structuralmember, wherein the structural members are parallel and form the sidesof tube with the cross sectional shape of an N-sided polygon and theframe members of each structural member have a shape that mates withframe members of adjacent structural members in a woodworking-type ofjoint at the corners of the N-sided polygon; polygonal cross-sectionframework wherein the frame members are concentric tubes with a crosssectional shape of N-sided polygonal ring; bullseye cross-sectionframework wherein the innermost frame member has a cross sectional shapeof an N-sided polygon and sits at the center of concentric N-sidedpolygonal cylindrical tubes formed by the other frame members; closednested shell framework wherein the frame members are closed nestedshells; curved framework wherein the frame members are curved;concentric ring framework wherein the frame members are concentricrings, each with an N-sided polygonal shape; insulative door; insulativewindow frame having a perimeter, the window frame comprising: aplurality insulative structural members, including the at least oneinsulative structural member, joined around the perimeter of the windowframe; insulative window having a perimeter, the window comprising: aplurality insulative structural members, including the at least oneinsulative structural member, joined around the perimeter of the windowand at least one sheet of material secured in an opening created by theframe members; insulative window having a perimeter, the windowcomprising: a plurality insulative structural members, including the atleast one insulative structural member, joined around the perimeter ofthe window and at least one insulating glass unit secured in an openingcreated by the frame members; panel structure comprising: spaced firstand second planar panels; and a plurality of spaced insulativestructural members connecting facing surfaces of the first and secondpanels, the plurality of spaced insulative structural members includingthe at least one insulative structural member; insulative structuralpanel having a front surface and back surface, the insulative structuralpanel comprising: a pair of spaced insulative structural members,including the at least one insulative structural member, having a firstlength, a depth extending between the front surface and back surface, awidth extending perpendicular to the depth, and spaced across in adirection of the width; and a hardenable insulative material disposedbetween the front surface and the rear surface in a direction of thedepth, between each of the spaced structural members in the direction ofthe width and substantially all of the space between the first andsecond frame members; wherein each insulative structural member is anembodiment of the insulative structural member further comprising: anynumber of additional frame members; any number of additional connectingmembers that each connect at least two members; any number of additionalframe members as part of the central frame member; any number ofadditional connecting members as part of the central frame member thateach connect at least two members; any number of protrusions that eachhave at least one point of connection to at least one other member, andany amount of insulative material between any number of frame members; afoil radiant barrier attached to any surface; additional members includeadditional frame members, and additional connecting members; membersinclude first connecting members, second connecting members, framemembers, protrusions, and additional members; connecting members includefirst connecting members, second connecting members, and protrusions;any number of the members are straight; any number of the members arecurved; any pair of the members are aligned; any pair of the members areparallel; any number of the members protrude in any directionperpendicular to any of the frame members; any number of the membersprotrude in a direction parallel to any of the frame members; any numberof the members comprise a plurality of elongated lamination memberssecured to adjacent elongated lamination members; any number of membersare made from a non-metallic material; any number of members are madefrom a wood-based material; any connecting member is any portion of awoodworking joint; any connecting member incorporates any portion of awoodworking joint; any frame member incorporates any portion of awoodworking joint; any frame member is any portion of a woodworkingjoint; any number of connecting members are offset from nearestneighboring connecting members along the length of a connected framemember; any number of connecting members have a substantially similarthickness to at least one of the frame members to which the connectingmember connects; any number of the connecting members run diagonallyrelative to a connected frame member; any number of the connectingmembers run parallel relative to a connected frame member; any number ofthe connecting members run perpendicular relative to a connected framemember; any number of the additional connecting members run diagonallyrelative to a connected frame member; any number of the additionalconnecting members run parallel relative to a connected frame member;any number of the additional connecting members run perpendicularrelative to a connected frame member.
 43. The insulative structuralmember of claim 42 being configured to make: the second span-wiseindirectness I2 greater than 5% (insulative aspect); the maximumcumulative distance between structural parts greater than 15% and lessthan {(60%±5%) times the first-direct-path span} (insulatable aspect butnot so insulatable that the structure becomes weak); and the second pathlength L2 less than 20 times the maximum cumulative distance betweenstructural parts (balance between the insulatable and insulativeaspects).
 44. A frame apparatus configured as one of: a first-typeinsulative window frame having a perimeter, the window frame comprising:a plurality of structural members joined around the perimeter of thewindow, each structural member comprising: a first frame member disposedalong an edge of the window on one side of the window; a second framemember disposed along the edge of the window on the opposite side of thewindow and spaced from and substantially parallel to the first framemember; and a connecting frame member between and contacting the firstand second frame members, the connecting frame members contacting thefirst frame members at a plurality of first locations and contacting thesecond frame members at a plurality of second locations, the first andsecond frame members having free interior-facing surfaces between thefirst and second locations; wherein any connecting frame member providesno direct path of conductive heat flow through the structural parts, ina direction perpendicular to the longitudinal direction, betweeninterior-facing surfaces of the first and second frame members; asecond-type insulative window frame having a perimeter, the window framecomprising: a plurality of structural members joined around theperimeter of the window, each structural member comprising: a firstframe member disposed along an edge of the window on one side of thewindow; a second frame member disposed along the edge of the window onthe opposite side of the window and spaced from and substantiallyparallel to the first frame member; and a connecting frame memberbetween and contacting the first and second frame members, theconnecting frame members contacting the first frame members at aplurality of first locations and contacting the second frame members ata plurality of second locations, the first and second frame membershaving free interior-facing surfaces between the first and secondlocations; a third-type insulative window frame having a perimeter, thewindow frame comprising: a plurality of structural members joined aroundthe perimeter of the window, each structural member comprising: a firstframe member disposed along an edge of the window on one side of thewindow; a second frame member disposed along the edge of the window onthe opposite side of the window and spaced from and substantiallyparallel to the first frame member; and a connecting frame memberbetween and contacting the first and second frame members, theconnecting frame members contacting the first frame members at aplurality of first locations and contacting the second frame members ata plurality of second locations, the first and second frame membershaving free interior-facing surfaces between the first and secondlocations; wherein each connecting frame member comprises: a centralframe member substantially parallel to the corresponding first andsecond frame members; a plurality of first connecting members connectingthe central frame member to at least the first frame member; and aplurality of second connecting members connecting the central framemember to at least the second frame member; and any connecting framemember provides no direct path of conductive heat flow through thestructural parts, in a direction perpendicular to the longitudinaldirection, between interior-facing surfaces of the first and secondframe members; a fourth-type insulative window frame having a perimeter,the window frame comprising: a plurality of structural members joinedaround the perimeter of the window, each structural member comprising: afirst frame member disposed along an edge of the window on one side ofthe window; a second frame member disposed along the edge of the windowon the opposite side of the window and spaced from and substantiallyparallel to the first frame member; and a connecting frame memberbetween and contacting the first and second frame members, theconnecting frame members contacting the first frame members at aplurality of first locations and contacting the second frame members ata plurality of second locations, the first and second frame membershaving free interior-facing surfaces between the first and secondlocations; wherein each connecting frame member comprises: a centralframe member substantially parallel to the corresponding first andsecond frame members; a plurality of first connecting members connectingthe central frame member to at least the first frame member; and aplurality of second connecting members connecting the central framemember to at least the second frame member; a fifth-type insulativewindow frame having a perimeter, the window frame comprising: aplurality of structural members joined around the perimeter of thewindow, each structural member comprising a connecting frame member, theconnecting frame member comprising: a first frame member disposed alongan edge of the window on one side of the window; a second frame memberdisposed along the edge of the window on the opposite side of the windowand spaced from and substantially parallel to the first frame member;and a set of at least one connecting member between and contacting thefirst and second frame members, the set of at least one connectingmember contacting the first frame member at a set of at least one firstlocation and contacting the second frame member at a set of at least onesecond location, the set of at least one connecting member being part ofa plurality of connecting members for all of the structural members, theset of at least one first location being part of a plurality of firstlocations for all of the structural members, and the set of at least onesecond location being part of a plurality of second locations for all ofthe structural members; wherein all of the first and second framemembers have free interior-facing surfaces between the first and secondlocations; and any connecting frame member provides no direct path ofconductive heat flow through the structural parts, in a directionperpendicular to the longitudinal direction, between interior-facingsurfaces of the first and second frame members; a sixth-type insulativewindow frame having a perimeter, the window frame comprising: aplurality of structural members joined around the perimeter of thewindow, each structural member comprising a connecting frame member, theconnecting frame member comprising: a first frame member disposed alongan edge of the window on one side of the window; a second frame memberdisposed along the edge of the window on the opposite side of the windowand spaced from and substantially parallel to the first frame member;and a set of at least one connecting member between and contacting thefirst and second frame members, the set of at least one connectingmember contacting the first frame member at a set of at least one firstlocation and contacting the second frame member at a set of at least onesecond location, the set of at least one connecting member being part ofa plurality of connecting members for all of the structural members, theset of at least one first location being part of a plurality of firstlocations for all of the structural members, and the set of at least onesecond location being part of a plurality of second locations for all ofthe structural members; wherein all of the first and second framemembers have free interior-facing surfaces between the first and secondlocations; a first-type panel structure comprising: spaced first andsecond planar panels; and a plurality of spaced structural membersconnecting facing surfaces of the first and second panels, each of thestructural members comprising: a first frame member in contact with thefirst planar panel in a longitudinal direction; a second frame member incontact with the second planar panel in the longitudinal direction, thesecond frame member being spaced from the first frame member andsubstantially parallel thereto; and a connecting frame member betweenand contacting the first and second frame members, the connecting framemember contacting the first frame member at a plurality of firstlocations and contacting the second frame member at a plurality ofsecond locations, the first and second frame members having freeinterior-facing surfaces between the first and second locations; whereinany connecting frame member provides no direct path of conductive heatflow through the structural parts, in a direction perpendicular to thelongitudinal direction, between interior-facing surfaces of the firstand second frame members; a second-type panel structure comprising:spaced first and second planar panels; and a plurality of spacedstructural members connecting facing surfaces of the first and secondpanels, each of the structural members comprising: a first frame memberin contact with the first planar panel in a longitudinal direction; asecond frame member in contact with the second planar panel in thelongitudinal direction, the second frame member being spaced from thefirst frame member and substantially parallel thereto; and a connectingframe member between and contacting the first and second frame members,the connecting frame member contacting the first frame member at aplurality of first locations and contacting the second frame member at aplurality of second locations, the first and second frame members havingfree interior-facing surfaces between the first and second locations; athird-type panel structure comprising: spaced first and second planarpanels; and a plurality of spaced structural members connecting facingsurfaces of the first and second panels, each of the structural memberscomprising: a first frame member in contact with the first planar panelin a longitudinal direction; a second frame member in contact with thesecond planar panel in the longitudinal direction, the second framemember being spaced from the first frame member and substantiallyparallel thereto; and a connecting frame member between and contactingthe first and second frame members, the connecting frame membercontacting the first frame member at a plurality of first locations andcontacting the second frame member at a plurality of second locations,the first and second frame members having free interior-facing surfacesbetween the first and second locations; secondary linking membersconnecting one of the spaced structural members to at least one otherspaced structural member wherein the secondary linking members provideno direct path of conductive heat flow between spaced structuralmembers; a fourth-type panel structure comprising: spaced first andsecond planar panels; and a plurality of spaced structural membersconnecting facing surfaces of the first and second panels, each of thestructural members comprising: a first frame member in contact with thefirst planar panel in a longitudinal direction; a second frame member incontact with the second planar panel in the longitudinal direction, thesecond frame member being spaced from the first frame member andsubstantially parallel thereto; and a connecting frame member betweenand contacting the first and second frame members, the connecting framemember contacting the first frame member at a plurality of firstlocations and contacting the second frame member at a plurality ofsecond locations, the first and second frame members having freeinterior-facing surfaces between the first and second locations;secondary linking members connecting one of the spaced structuralmembers to at least one other spaced structural member; a fifth-typepanel structure comprising: spaced first and second planar panels; and aplurality of spaced structural members connecting facing surfaces of thefirst and second panels, each of the structural members comprising: afirst frame member in contact with the first planar panel in alongitudinal direction; a second frame member in contact with the secondplanar panel in the longitudinal direction, the second frame memberbeing spaced from the first frame member and substantially parallelthereto; and a connecting frame member between and contacting the firstand second frame members, the connecting frame member contacting thefirst frame member at a plurality of first locations and contacting thesecond frame member at a plurality of second locations, the first andsecond frame members having free interior-facing surfaces between thefirst and second locations; wherein the connecting frame membercomprises a central frame member substantially parallel to the first andsecond frame members and a plurality of linking members perpendicular tothe central frame members in contact with the first and second framemembers at the first and second locations; and any connecting framemember provides no direct path of conductive heat flow through thestructural parts, in a direction perpendicular to the longitudinaldirection, between interior-facing surfaces of the first and secondframe members; a sixth-type panel structure comprising: spaced first andsecond planar panels; and a plurality of spaced structural membersconnecting facing surfaces of the first and second panels, each of thestructural members comprising: a first frame member in contact with thefirst planar panel in a longitudinal direction; a second frame member incontact with the second planar panel in the longitudinal direction, thesecond frame member being spaced from the first frame member andsubstantially parallel thereto; and a connecting frame member betweenand contacting the first and second frame members, the connecting framemember contacting the first frame member at a plurality of firstlocations and contacting the second frame member at a plurality ofsecond locations, the first and second frame members having freeinterior-facing surfaces between the first and second locations; whereinthe connecting frame member comprises: a central frame membersubstantially parallel to the first and second frame members and aplurality of linking members perpendicular to the central frame membersin contact with the first and second frame members at the first andsecond locations; a seventh-type panel structure comprising: spacedfirst and second planar panels; and a plurality of spaced structuralmembers connecting facing surfaces of the first and second panels, eachof the structural members comprising: a first frame member in contactwith the first planar panel in a longitudinal direction; a second framemember in contact with the second planar panel in the longitudinaldirection, the second frame member being spaced from the first framemember and substantially parallel thereto; and a connecting frame memberbetween and contacting the first and second frame members, theconnecting frame member contacting the first frame member at a pluralityof first locations and contacting the second frame member at a pluralityof second locations, the first and second frame members having freeinterior-facing surfaces between the first and second locations; whereinthe connecting frame member comprises: a central frame membersubstantially parallel to the first and second frame members; and aplurality of linking members perpendicular to the central frame membersin contact with the first and second frame members at the first andsecond locations; and any connecting frame member provides no directpath of conductive heat flow through the structural parts, in adirection perpendicular to the longitudinal direction, betweeninterior-facing surfaces of the first and second frame members; aneighth-type panel structure comprising: spaced first and second planarpanels; and a plurality of spaced structural members connecting facingsurfaces of the first and second panels, each of the structural memberscomprising: a first frame member in contact with the first planar panelin a longitudinal direction; a second frame member in contact with thesecond planar panel in the longitudinal direction, the second framemember being spaced from the first frame member and substantiallyparallel thereto; and a connecting frame member between and contactingthe first and second frame members, the connecting frame membercontacting the first frame member at a plurality of first locations andcontacting the second frame member at a plurality of second locations,the first and second frame members having free interior-facing surfacesbetween the first and second locations; wherein the connecting framemember comprises: a central frame member substantially parallel to thefirst and second frame members and a plurality of linking membersperpendicular to the central frame members in contact with the first andsecond frame members at the first and second locations; a first-typelattice framework comprising: a first frame member; a second framemember; a first plurality of frame members including the first framemember; a second plurality of frame members including the second framemember; a plurality of laterally spaced structural members eachcomprising: a connecting frame member positioned between and contactingthe first and second plurality of frame members, the connecting framemember comprising: a central frame member, the central frame membercomprising a third frame member, fourth frame member, and a plurality offirst connecting members, the first connecting member joining at leastthe third frame member to the fourth frame member, the third framemember contacting the first plurality of frame members at a plurality offirst locations, the fourth frame member contacting the second pluralityof frame members at a plurality of second locations, each of the framemembers in the first and second plurality of frame members having freeinterior-facing surfaces between the first and second locations; whereinany connecting frame member provides no direct path of conductive heatflow through the structural parts, in a direction perpendicular to thelongitudinal direction, between interior-facing surfaces of the firstand second frame members; a second-type lattice framework comprising: afirst frame member; a second frame member; a first plurality of framemembers including the first frame member; a second plurality of framemembers including the second frame member; a plurality of laterallyspaced structural members each comprising: a connecting frame memberpositioned between and contacting the first and second plurality offrame members, the connecting frame member comprising: a central framemember, the central frame member comprising a third frame member, fourthframe member, and a plurality of first connecting members, the firstconnecting member joining at least the third frame member to the fourthframe member, the third frame member contacting the first plurality offrame members at a plurality of first locations, the fourth frame membercontacting the second plurality of frame members at a plurality ofsecond locations, each of the frame members in the first and secondplurality of frame members having free interior-facing surfaces betweenthe first and second locations; a first-type insulative structural panelhaving a front surface and back surface, the insulative structural panelcomprising: a pair of spaced structural members having a first length, adepth extending between the front surface and back surface, a widthextending perpendicular to the depth, and spaced across in a directionof the width, each spaced structural member comprising: a firstelongated frame member positioned along the back surface and extendingin the direction of the spaced structural member length; a secondelongated frame member positioned along the front surface spaced fromand substantially parallel to the first elongated frame member, thesecond elongated frame member having a second length substantially thesame as the first length; a central elongated frame member spacedbetween and parallel to the first and second frame members, the centralframe member having a third length substantially the same as the firstlength; a plurality of first connecting members joining the firstelongated member to one surface of the central frame member, the firstconnecting members having a connection length shorter than the firstlength; and a plurality of second connecting members joining the secondelongated member to an opposite surface of the central frame member, thesecond connecting members having a connection length substantiallyshorter than the first length; a connecting frame member comprising thefirst connecting members, second connecting members, as well as thecentral frame member; and a hardenable insulative material disposedbetween the front surface and the rear surface in a direction of thedepth, between each of the spaced structural members in the direction ofthe width and substantially all of the space between the first andsecond frame members; wherein any connecting frame member provides nodirect path of conductive heat flow through the structural parts, in adirection perpendicular to the longitudinal direction, betweeninterior-facing surfaces of the first and second frame members; asecond-type insulative structural panel having a front surface and backsurface, the insulative structural panel comprising: a pair of spacedstructural members having a first length, a depth extending between thefront surface and back surface, a width extending perpendicular to thedepth, and spaced across in a direction of the width, each spacedstructural member comprising: a first elongated frame member positionedalong the back surface and extending in the direction of the spacedstructural member length; a second elongated frame member positionedalong the front surface spaced from and substantially parallel to thefirst elongated frame member, the second elongated frame member having asecond length substantially the same as the first length; a centralelongated frame member spaced between and parallel to the first andsecond frame members, the central frame member having a third lengthsubstantially the same as the first length; a plurality of firstconnecting members joining the first elongated member to one surface ofthe central frame member, the first connecting members having aconnection length shorter than the first length; and a plurality ofsecond connecting members joining the second elongated member to anopposite surface of the central frame member, the second connectingmembers having a connection length substantially shorter than the firstlength; a connecting frame member comprising the first connectingmembers, second connecting members, as well as the central frame member;and a hardenable insulative material disposed between the front surfaceand the rear surface in a direction of the depth, between each of thespaced structural members in the direction of the width andsubstantially all of the space between the first and second framemembers; a first-type structural member for connecting a first and asecond panel to make a panel structure, the structural membercomprising: a first elongated frame member; a second elongated framemember spaced from and substantially parallel to the first elongatedframe member; and a connecting frame member between and contacting thefirst and second frame members, the connecting frame member contactingthe first frame member at a plurality of first locations and contactingthe second frame member at a plurality of second locations, the firstand second frame members having free interior-facing surfaces betweenthe first and second locations; wherein the connecting frame memberprovides no direct path of conductive heat flow through the structuralparts, in a direction perpendicular to the longitudinal direction,between interior-facing surfaces of the first and second frame members;a second-type structural member comprising: a first elongated framemember; a second elongated frame member spaced from and substantiallyparallel to the first elongated frame member; and a connecting framemember between and contacting the first and second frame members, theconnecting frame member contacting the first frame member at a pluralityof first locations and contacting the second frame member at a pluralityof second locations, the first and second frame members having freeinterior-facing surfaces between the first and second locations; athird-type structural member comprising a connecting frame member, theconnecting frame member comprising: a first elongated frame member; asecond elongated frame member spaced from and substantially parallel tothe first elongated frame member; and a plurality of connecting memberscontacting the first frame member at a plurality of first locations andcontacting the second frame member at a plurality of second locations,wherein each connecting member is positioned between the first andsecond frame members, has a face running parallel to and contacting aninward facing surface of the first frame member at one of the firstlocations, and has an opposing face running parallel to and contactingan inward facing surface of the second frame member at one of the secondlocations; wherein the connecting frame member provides no direct pathof conductive heat flow through the structural parts, in a directionperpendicular to the longitudinal direction, between interior-facingsurfaces of the first and second frame members; a fourth-type structuralmember comprising a connecting frame member, the connecting frame membercomprising: a first elongated frame member; a second elongated framemember spaced from and substantially parallel to the first elongatedframe member; and a plurality of connecting members contacting the firstframe member at a plurality of first locations and contacting the secondframe member at a plurality of second locations, wherein each connectingmember is positioned between the first and second frame members, has aface running parallel to and contacting an inward facing surface of thefirst frame member at one of the first locations, and has an opposingface running parallel to and contacting an inward facing surface of thesecond frame member at one of the second locations; a fifth-typestructural member comprising a connecting frame member, the connectingframe member comprising: a first elongated frame member; a secondelongated frame member spaced from and substantially parallel to thefirst elongated frame member; and a plurality of connecting memberscontacting the first frame member at a plurality of first locations andcontacting the second frame member at a plurality of second locations,each of the connecting members joining at least the first and secondelongated frame members and running diagonally at an angle of less than32° relative to the first elongated frame member to reduce conductiveheat flow between the first and second elongated frame members; asixth-type structural member comprising a connecting frame member, theconnecting frame member comprising: a first elongated frame member; asecond elongated frame member spaced from and substantially parallel tothe first elongated frame member; and a plurality of connecting memberscontacting the first frame member at a plurality of first locations andcontacting the second frame member at a plurality of second locations,each of the connecting members joining at least the first and secondelongated frame members and running diagonally at an angle of less than32° relative to the first elongated frame member to reduce conductiveheat flow between the first and second elongated frame members; afirst-type insulative structural member comprising: a first elongatedframe member having a first length; a second elongated frame memberspaced from and substantially parallel to the first elongated framemember, the second elongated frame member having a second lengthsubstantially the same as the first length; a central elongated framemember spaced between and parallel to the first and second framemembers, the central frame member having a third length substantiallythe same as the first length; a plurality of first connecting membersjoining the first elongated frame member to one surface of the centralframe member, the first connecting members having a connection lengthshorter than the first length; and a plurality of second connectingmembers joining the second elongated frame member to an opposite surfaceof the central frame member, the second connecting members having aconnection length substantially shorter than the first length; whereinthe plurality of first connecting members, the plurality of secondconnecting members, and the central elongated frame member constitute aconnecting frame member contacting the first frame member at a pluralityof first locations where the first connecting members contact the firstframe member and contacting the second frame member at a plurality ofsecond locations where the second connecting members contact the secondframe member; the connecting frame member is configured to give a firstdirect path between an outside surface of the first elongated framemember an opposing outside surface of the second elongated frame memberwith a second span and a first cumulative distance between structuralparts (a) greater than {(9%±1%) times the second span} (insulatableaspect) and (b) less than {80% times the second span} (insulatableaspect but not so insulatable that the structure becomes weak) whereinthe first cumulative distance between structural parts is less than anyother cumulative distance between structural parts for any direct pathbetween the interior and exterior surfaces; and a second-type insulativestructural member comprising: a first elongated frame member having afirst length; a second elongated frame member spaced from andsubstantially parallel to the first elongated frame member, the secondelongated frame member having a second length substantially the same asthe first length; a central elongated frame member spaced between andparallel to the first and second frame members, the central frame memberhaving a third length substantially the same as the first length; aplurality of first connecting members joining the first elongated framemember to one surface of the central frame member, the first connectingmembers having a connection length shorter than the first length; and aplurality of second connecting members joining the second elongatedframe member to an opposite surface of the central frame member, thesecond connecting members having a connection length substantiallyshorter than the first length; wherein the connecting members provide nodirect path of conductive heat flow through the structural parts, in adirection perpendicular to the longitudinal direction, betweeninterior-facing surfaces of the first and second frame members; theplurality of first connecting members, the plurality of secondconnecting members, and the central elongated frame member constitute aconnecting frame member contacting the first frame member at a pluralityof first locations where the first connecting members contact the firstframe member and contacting the second frame member at a plurality ofsecond locations where the second connecting members contact the secondframe member; a third-type insulative structural member comprising: afirst elongated frame member having a first length; a second elongatedframe member spaced from and substantially parallel to the firstelongated frame member, the second elongated frame member having asecond length substantially the same as the first length; a centralelongated frame member spaced between and parallel to the first andsecond frame members, the central frame member having a third lengthsubstantially the same as the first length; a plurality of firstconnecting members joining the first elongated frame member to onesurface of the central frame member, the first connecting members havinga connection length shorter than the first length; and a plurality ofsecond connecting members joining the second elongated frame member toan opposite surface of the central frame member, the second connectingmembers having a connection length substantially shorter than the firstlength; wherein the plurality of first connecting members, the pluralityof second connecting members, and the central elongated frame memberconstitute a connecting frame member contacting the first frame memberat a plurality of first locations where the first connecting memberscontact the first frame member and contacting the second frame member ata plurality of second locations where the second connecting memberscontact the second frame member; a fourth-type insulative structuralmember comprising: a first elongated frame member having a first length;a second elongated frame member spaced from and substantially parallelto the first elongated frame member, the second elongated frame memberhaving a second length substantially the same as the first length; acentral elongated frame member spaced between and parallel to the firstand second frame members, the central frame member having a third lengthsubstantially the same as the first length; a plurality of firstconnecting members joining at least the first elongated frame member tothe central frame member, the first connecting members having aconnection length shorter than the first length; and a plurality ofsecond connecting members joining at least the second elongated framemember to the central frame member, the second connecting members havinga connection length substantially shorter than the first length; whereinthe connecting members provide no direct path of conductive heat flowthrough the structural parts, in a direction perpendicular to thelongitudinal direction, between interior-facing surfaces of the firstand second frame members; the plurality of first connecting members, theplurality of second connecting members, and the central elongated framemember constitute a connecting frame member contacting the first framemember at a plurality of first locations where the first connectingmembers contact the first frame member and contacting the second framemember at a plurality of second locations where the second connectingmembers contact the second frame member; a fifth-type insulativestructural member comprising: a first elongated frame member having afirst length; a second elongated frame member spaced from andsubstantially parallel to the first elongated frame member, the secondelongated frame member having a second length substantially the same asthe first length; a central elongated frame member spaced between andparallel to the first and second frame members, the central frame memberhaving a third length substantially the same as the first length; aplurality of first connecting members joining at least the firstelongated frame member to the central frame member, the first connectingmembers having a connection length shorter than the first length; and aplurality of second connecting members joining at least the secondelongated frame member to the central frame member, the secondconnecting members having a connection length substantially shorter thanthe first length; wherein the plurality of first connecting members, theplurality of second connecting members, and the central elongated framemember constitute a connecting frame member contacting the first framemember at a plurality of first locations where the first connectingmembers contact the first frame member and contacting the second framemember at a plurality of second locations where the second connectingmembers contact the second frame member and an first-type insulativebuilding block comprising: a first elongated frame member; a secondelongated frame member spaced from and substantially parallel to thefirst elongated frame member; and a connecting frame member between andcontacting the first and second frame members, the connecting framemember contacting the first frame member at a plurality of firstlocations and contacting the second frame member at a plurality ofsecond locations, the first and second frame members having freeinterior-facing surfaces between the first and second locations;wherein: the connecting frame member, first elongated frame member, andsecond elongated frame member are integrally formed; and can be stackedin a running bond configuration with other replicas of itself to createa block wall structure with an spanwise indirectness greater than 50%for the most-direct metric path between exterior facing surfaces of theblock wall structure; an second-type insulative building blockcomprising: a first elongated frame member; a second elongated framemember spaced from and substantially parallel to the first elongatedframe member; and a connecting frame member between and contacting thefirst and second frame members, the connecting frame member contactingthe first frame member at a plurality of first locations and contactingthe second frame member at a plurality of second locations, the firstand second frame members having free interior-facing surfaces betweenthe first and second locations; wherein: the connecting frame member,first elongated frame member, and second elongated frame member areintegrally formed; and can be stacked in a running bond configurationwith other replicas of itself to create a block wall structure with anspanwise indirectness greater than 50% for the most-direct metric pathbetween exterior facing surfaces of the block wall structure; the frameapparatus providing: a first direct path between exterior-facingsurfaces of any connected first and second frame members with afirst-direct-path span and a maximum cumulative distance betweenstructural parts that is greater than any other cumulative distancebetween structural parts for any direct path between exterior-facingsurfaces of any connected first and second frame members; a firstmost-direct metric path between any connected first elongated framemember and second elongated frame member with a first path length L1, afirst span S1, and a first span-wise indirectness I1={L1/S1}−1 that isless than any other span-wise indirectness for any other most-directmetric path between any connected first and second frame members; asecond most-direct metric path between any connected first elongatedframe member and second elongated frame member with a second path lengthL2, a second span S2, and a second span-wise indirectness I2={L2/52}−1that is less than any other span-wise indirectness for any othermost-direct metric path between any connected first and second framemembers in the same bundle of metric paths but is greater than any otherminimum value of span-wise indirectness for any other bundle of metricpaths; wherein: the second-type insulative window frame, fourth-typeinsulative window frame, sixth-type insulative window frame, second-typepanel structure, fourth-type panel structure, sixth-type panelstructure, eighth-type panel structure, second-type lattice framework,second-type insulative structural panel, second-type structural member,fourth-type structural member, sixth-type structural member, third-typeinsulative structural member, fifth-type insulative structural member,second-type insulative building block are configured to make the maximumcumulative distance between structural parts less than {80% times thefirst-direct-path span} (insulatable aspect but not so insulatable thatthe structure becomes weak); the structural parts include the elongatedframe members, connecting frame members, plurality of first connectingmembers, plurality of second connecting members, linking members, andsecondary linking members.
 45. The frame apparatus of claim 44, furthercomprising any number of additional structural members; any number ofadditional structural members disposed parallel to the other structuralmembers; any number additional spaced structural member disposed at anangle relative to the other structural members; any number additionalspaced structural member disposed at an angle relative to the otherstructural members and attached at each end to a pair of spacedstructural members; any number of additional frame members; any numberof additional connecting members that each connect at least two members;any number of additional linking members that each connect at least twomembers; any number of additional secondary linking members that eachconnect at least two structural members; any number of additional framemembers as part of any connecting frame member; any number of additionalconnecting members as part of any connecting frame member that eachconnect at least two members; any number of protrusions that each haveat least one point of connection to at least one other member; anyamount of insulative material between any number of frame members; anyamount of hardenable insulative material between any number of framemembers; any amount of closed cell foam between any number of framemembers; a foil radiant barrier attached to any surface; wherein:additional members include additional frame members, additionalconnecting members, additional linking members, and additional secondarylinking members; members include first connecting members, secondconnecting members, frame members, linking members, secondary linkingmembers, protrusions, and additional members; connecting members includefirst connecting members, second connecting members, linking members,secondary linking members, and protrusions; any number of the membersare straight; any number of the members are curved; any pair of themembers are aligned; any pair of the members are parallel; any number ofthe members protrude in any direction perpendicular to any of the framemembers; any number of the members protrude in a direction parallel toany of the frame members; any number of the members comprise a pluralityof elongated lamination members secured to adjacent elongated laminationmembers; any number of members are made from a non-metallic material;any number of members are made from a wood-based material; anyconnecting member is any portion of a woodworking joint; any connectingmember incorporates any portion of a woodworking joint; any frame memberincorporates any portion of a woodworking joint; any frame member is anyportion of a woodworking joint; any number of connecting members areoffset from nearest neighboring connecting members along the length of aconnected frame member; any number of connecting members have asubstantially similar thickness to at least one of the frame members towhich the connecting member connects; any number of the connectingmembers run diagonally relative to a connected frame member; any numberof the connecting members run parallel relative to a connected framemember; any number of the connecting members run perpendicular relativeto a connected frame member; any number of the additional connectingmembers run diagonally relative to a connected frame member; any numberof the additional connecting members run parallel relative to aconnected frame member; any number of the additional connecting membersrun perpendicular relative to a connected frame member; the frameapparatus is configured to make the second span-wise indirectness I2greater than 5% (insulative aspect); the frame apparatus is configuredto make the second path length L2 less than 20 times the maximumcumulative distance between structural parts (balance between theinsulatable and insulative aspects); and any connecting frame member isconfigured to make the maximum cumulative distance between structuralparts less than {80% times the first-direct-path span} (insulatableaspect but not so insulatable that the structure becomes weak).
 46. Theframe apparatus of claim 44 further comprising any number of additionalstructural members; any number of additional structural members disposedparallel to the other structural members; any number additional spacedstructural member disposed at an angle relative to the other structuralmembers; any number additional spaced structural member disposed at anangle relative to the other structural members and attached at each endto a pair of spaced structural members; any number of additional framemembers; any number of additional connecting members that each connectat least two members, any number of additional linking members that eachconnect at least two members; any number of additional secondary linkingmembers that each connect at least two structural members; any number ofadditional frame members as part of any connecting frame member; anynumber of additional connecting members as part of any connecting framemember that each connect at least two members; any number of protrusionsthat each have at least one point of connection to at least one othermember; any amount of insulative material between any number of framemembers; any amount of hardenable insulative material between any numberof frame members; any amount of closed cell foam between any number offrame members; a foil radiant barrier attached to any surface; wherein:additional members include additional frame members, additionalconnecting members, additional linking members, and additional secondarylinking members; members include first connecting members, secondconnecting members, frame members, linking members, secondary linkingmembers, protrusions, and additional members; connecting members includefirst connecting members, second connecting members, linking members,secondary linking members, and protrusions; any number of the membersare straight; any number of the members are curved; any pair of themembers are aligned; any pair of the members are parallel; any number ofthe members protrude in any direction perpendicular to any of the framemembers; any number of the members protrude in a direction parallel toany of the frame members; any number of the members comprise a pluralityof elongated lamination members secured to adjacent elongated laminationmembers; any number of members are made from a non-metallic material;any number of members are made from a wood-based material; anyconnecting member is any portion of a woodworking joint; any connectingmember incorporates any portion of a woodworking joint; any frame memberincorporates any portion of a woodworking joint; any frame member is anyportion of a woodworking joint; any number of connecting members areoffset from nearest neighboring connecting members along the length of aconnected frame member; any number of connecting members have asubstantially similar thickness to at least one of the frame members towhich the connecting member connects; any number of the connectingmembers run diagonally relative to a connected frame member; any numberof the connecting members run parallel relative to a connected framemember; any number of the connecting members run perpendicular relativeto a connected frame member; any number of the additional connectingmembers run diagonally relative to a connected frame member; any numberof the additional connecting members run parallel relative to aconnected frame member; and any number of the additional connectingmembers run perpendicular relative to a connected frame member.
 47. Theframe apparatus of claim 46 wherein the connection length of any of theplurality of first locations and any of the plurality of secondlocations is less than 20% of the length of the first elongated framemember.
 48. The frame apparatus of claim 46 wherein the distance betweenfirst locations is at least 2 times the distance between the first andsecond frame members and the distance between second locations is atleast 2 times the distance between the first and second frame members.49. The frame apparatus of claim 46 wherein any connecting frame memberhas diagonally extending features between the first frame member and thesecond frame member.
 50. The frame apparatus of claim 46 beingconfigured to make the first span-wise I1 greater than 8% (insulativeaspect).
 51. The frame apparatus of claim 46 being configured to makethe maximum cumulative distance between structural parts greater than{(15%±1%) times the first-direct-path span} (insulatable aspect) andless than {65% times the second-direct-path span} (insulatable aspectbut not so insulatable that the structure becomes weak).
 52. The frameapparatus of claim 46 being configured to make the first path length L1less than 40 times the maximum cumulative distance between structuralparts (balance between the insulatable and insulative aspects) whereinthe structural parts include the first elongated frame member, secondelongated frame member, and connecting frame member.